{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run 3.4-common.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 0: w = tensor([0.5210]) b = tensor([0.8223]) \n",
      "MSE Error = 1327.32177734375\n",
      "Gradient of w: tensor([-398.0006]) \n",
      "Gradient of b: tensor([-52.3423])\n",
      "Step 100: w = tensor([7.4348]) b = tensor([-4.4308]) \n",
      "MSE Error = 74.19503784179688\n",
      "Gradient of w: tensor([-0.7114]) \n",
      "Gradient of b: tensor([4.6875])\n",
      "Step 200: w = tensor([7.9912]) b = tensor([-8.0973]) \n",
      "MSE Error = 60.17138671875\n",
      "Gradient of w: tensor([-0.4234]) \n",
      "Gradient of b: tensor([2.7899])\n",
      "Step 300: w = tensor([8.3224]) b = tensor([-10.2795]) \n",
      "MSE Error = 55.203895568847656\n",
      "Gradient of w: tensor([-0.2520]) \n",
      "Gradient of b: tensor([1.6604])\n",
      "Step 400: w = tensor([8.5195]) b = tensor([-11.5783]) \n",
      "MSE Error = 53.444305419921875\n",
      "Gradient of w: tensor([-0.1500]) \n",
      "Gradient of b: tensor([0.9882])\n",
      "Step 500: w = tensor([8.6368]) b = tensor([-12.3512]) \n",
      "MSE Error = 52.821014404296875\n",
      "Gradient of w: tensor([-0.0893]) \n",
      "Gradient of b: tensor([0.5882])\n",
      "Step 600: w = tensor([8.7066]) b = tensor([-12.8113]) \n",
      "MSE Error = 52.60023498535156\n",
      "Gradient of w: tensor([-0.0531]) \n",
      "Gradient of b: tensor([0.3501])\n",
      "Step 700: w = tensor([8.7481]) b = tensor([-13.0851]) \n",
      "MSE Error = 52.522029876708984\n",
      "Gradient of w: tensor([-0.0316]) \n",
      "Gradient of b: tensor([0.2083])\n",
      "Step 800: w = tensor([8.7729]) b = tensor([-13.2480]) \n",
      "MSE Error = 52.494327545166016\n",
      "Gradient of w: tensor([-0.0188]) \n",
      "Gradient of b: tensor([0.1240])\n",
      "Step 900: w = tensor([8.7876]) b = tensor([-13.3450]) \n",
      "MSE Error = 52.484500885009766\n",
      "Gradient of w: tensor([-0.0112]) \n",
      "Gradient of b: tensor([0.0738])\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True function: y=x^2 -x + 2\n",
      "Learnt function: y_pred = 8.796333312988281*x + -13.40276050567627\n",
      "Clearly the model is not converging to anything\n",
      "close to the desired/true function.\n",
      "Our model architecture is inadequate\n"
     ]
    }
   ],
   "source": [
    "# This programming exercise is similar to the last\n",
    "# one in that we will fit a model to a set of\n",
    "# observations from a known function with small added\n",
    "# noise.\n",
    "# However, here, that known function is non-linear.\n",
    "#\n",
    "# Here the input data is generated from non-linear\n",
    "# function y = x^2 -x + 2.\n",
    "# As before, our observations (training data) comprise\n",
    "# various values of x and corresponding values of y\n",
    "# computed from this function.\n",
    "# We will add some noise to the computed values to\n",
    "# generate the observed value.\n",
    "#\n",
    "# We will train a model y_obs = w_0*x^2 + w_1*x + b\n",
    "# and see if the learnt parameters come out close to\n",
    "# the expected values w_0 = 1, w_1 = -1 b = 2.\n",
    "\n",
    "\n",
    "torch.manual_seed(0)\n",
    "N = 100\n",
    "\n",
    "# Generate random x values\n",
    "x = 10 * torch.rand(N, 1)\n",
    "\n",
    "# Compute true function outputs \n",
    "y = x**2 - x + 2.0\n",
    "\n",
    "# Add some random noise to get observed values of y\n",
    "y_obs = y + (0.5 * torch.rand(N, 1) - 0.25)\n",
    "\n",
    "# Plot the true function and the data points.\n",
    "# True y values (magenta) will fall on a parabola.\n",
    "# The noise-added observed values (green points)\n",
    "#  will fall around that parabola.\n",
    "plt.scatter(x.data, y_obs.data, color=\"green\")\n",
    "draw_parabola(2, -1, 1)\n",
    "plt.title('True function + data points')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()\n",
    "\n",
    "# First, let us try a\n",
    "# linear model y_pred = wx + b\n",
    "w = torch.rand(1, requires_grad=True)\n",
    "b = torch.rand(1, requires_grad=True)\n",
    "\n",
    "params = [b, w]\n",
    "num_steps = 1000\n",
    "learning_rate = 1e-2\n",
    "\n",
    "plt.figure()\n",
    "i = 1\n",
    "plot_steps = [0, 50, 100, 999]\n",
    "\n",
    "# Train model iteratively\n",
    "for step in range(num_steps):\n",
    "    # linear model\n",
    "    y_pred = params[0] + params[1] * x\n",
    "    \n",
    "    # Periodically plot the true function and\n",
    "    # current approximation to check how we are doing    \n",
    "    if step in plot_steps:\n",
    "        draw_subplot(i, step, draw_parabola, \n",
    "                     {\"w0\": 2, \"w1\": -1, \"w2\": 1},\n",
    "                    draw_line,\n",
    "                    {\"m\": params[1].data.numpy()[0],\n",
    "                     \"c\": params[0].data.numpy()[0],\n",
    "                     \"color\":\"blue\",\n",
    "                     \"label\": \"y_pred=%0.2fx+%0.2f\"\\\n",
    "                                %(params[1].data.numpy()[0],\n",
    "                                  params[0].data.numpy()[0])} \n",
    "                    )\n",
    "        i+=1\n",
    "        \n",
    "    # Compute Mean Squared Error (M.S.E)\n",
    "    # i.e (y_pred - y_obs)^2\n",
    "    mean_squared_error = torch.mean((y_pred\n",
    "                                     - y_obs) ** 2)\n",
    "    \n",
    "    # Back propogate. Computes the partial derivative\n",
    "    # of error with respect to each variable and stores it\n",
    "    # within the grad field of the variable.\n",
    "    mean_squared_error.backward()\n",
    "    \n",
    "    # Print some diagnostic values every 100th iteration\n",
    "    if step % 100 == 0:\n",
    "        print(\"Step {}: w = {} b = {} \\nMSE Error = {}\"\\\n",
    "              .format(step, params[1].data,\n",
    "                      params[0].data,\n",
    "                      mean_squared_error))\n",
    "        print(\"Gradient of w: {} \\nGradient of b: {}\"\\\n",
    "              .format(params[1].grad, params[0].grad))\n",
    "        \n",
    "    # Crucial step, adjust the parameters (weights and bias)\n",
    "    # using the gradients (partial derivatives) computed during\n",
    "    # the call to backward() above        \n",
    "    update_parameters(params, learning_rate)\n",
    "    \n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"True function: y=x^2 -x + 2\")\n",
    "print(\"Learnt function: y_pred = {}*x + {}\"\\\n",
    "      .format(params[1].data.numpy()[0],\n",
    "              params[0].data.numpy()[0]))\n",
    "print(\"Clearly the model is not converging to anything\\n\"\n",
    "      \"close to the desired/true function.\\n\"\n",
    "      \"Our model architecture is inadequate\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 0:\n",
      "w0 = tensor([1.4875]) w1 = tensor([-0.2230]) w2 = tensor([-1.0057])\n",
      "MSE Error = 7090.93505859375\n",
      "Gradient of w0: tensor([-123.5347]) \n",
      "Gradient of w1: tensor([-927.7972])\n",
      "Gradient of w1: tensor([-7398.9434])\n",
      "Step 20000:\n",
      "w0 = tensor([1.4473]) w1 = tensor([-0.7683]) w2 = tensor([0.9801])\n",
      "MSE Error = 0.044630616903305054\n",
      "Gradient of w0: tensor([-0.0930]) \n",
      "Gradient of w1: tensor([0.0411])\n",
      "Gradient of w1: tensor([-0.0038])\n",
      "Step 40000:\n",
      "w0 = tensor([1.6002]) w1 = tensor([-0.8353]) w2 = tensor([0.9859])\n",
      "MSE Error = 0.030484532937407494\n",
      "Gradient of w0: tensor([-0.0619]) \n",
      "Gradient of w1: tensor([0.0271])\n",
      "Gradient of w1: tensor([-0.0023])\n",
      "Step 60000:\n",
      "w0 = tensor([1.7020]) w1 = tensor([-0.8798]) w2 = tensor([0.9898])\n",
      "MSE Error = 0.024226026609539986\n",
      "Gradient of w0: tensor([-0.0412]) \n",
      "Gradient of w1: tensor([0.0181])\n",
      "Gradient of w1: tensor([-0.0015])\n",
      "Step 80000:\n",
      "w0 = tensor([1.7696]) w1 = tensor([-0.9094]) w2 = tensor([0.9924])\n",
      "MSE Error = 0.021457994356751442\n",
      "Gradient of w0: tensor([-0.0274]) \n",
      "Gradient of w1: tensor([0.0120])\n",
      "Gradient of w1: tensor([-0.0008])\n",
      "Step 100000:\n",
      "w0 = tensor([1.8146]) w1 = tensor([-0.9291]) w2 = tensor([0.9941])\n",
      "MSE Error = 0.020232772454619408\n",
      "Gradient of w0: tensor([-0.0182]) \n",
      "Gradient of w1: tensor([0.0080])\n",
      "Gradient of w1: tensor([-0.0007])\n",
      "Step 120000:\n",
      "w0 = tensor([1.8444]) w1 = tensor([-0.9421]) w2 = tensor([0.9953])\n",
      "MSE Error = 0.019691618159413338\n",
      "Gradient of w0: tensor([-0.0121]) \n",
      "Gradient of w1: tensor([0.0054])\n",
      "Gradient of w1: tensor([-0.0003])\n",
      "Step 140000:\n",
      "w0 = tensor([1.8643]) w1 = tensor([-0.9508]) w2 = tensor([0.9960])\n",
      "MSE Error = 0.019450880587100983\n",
      "Gradient of w0: tensor([-0.0081]) \n",
      "Gradient of w1: tensor([0.0036])\n",
      "Gradient of w1: tensor([-0.0004])\n",
      "Step 160000:\n",
      "w0 = tensor([1.8775]) w1 = tensor([-0.9566]) w2 = tensor([0.9965])\n",
      "MSE Error = 0.019344843924045563\n",
      "Gradient of w0: tensor([-0.0053]) \n",
      "Gradient of w1: tensor([0.0026])\n",
      "Gradient of w1: tensor([-0.0002])\n",
      "Step 180000:\n",
      "w0 = tensor([1.8861]) w1 = tensor([-0.9604]) w2 = tensor([0.9969])\n",
      "MSE Error = 0.019298240542411804\n",
      "Gradient of w0: tensor([-0.0037]) \n",
      "Gradient of w1: tensor([0.0015])\n",
      "Gradient of w1: tensor([-0.0003])\n"
     ]
    },
    {
     "data": {
      "image/png": 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WrYuvry+jR4/m3Llztzz2/fffp1GjRtjb2xMcHMzevXtN9mdlZTF58mTq1auHk5MTgwYNKrSUqLllZWXx2GOP0bJlS2xsbPTJ/W/l0qVLjBgxAhcXF9zc3Bg/fjwZGabL6vz222906dIFe3t7/Pz8eOONN8pfYCPa3csTaE3lzkALtFHkpbB06VK6du2Ki4sLBoOh1PMlVuZ7N2fOHJYuXcqSJUuIioriiSeeKJQnMjKS/v374+PjQ926dWnTpg2rVq26redTag8VvzQWi1+3cgbECCestEE+Li5w40QIKn5VMaKUSVpamgCSlpZWaN+1a9ckISFBrl27ZoGSVR2pqakSGhoqX375pRw+fFiioqKkY8eO0q5duxKPW7Nmjdja2sonn3wiBw8elAkTJoibm5skJyfreZ544gnx8/OTbdu2ya+//ir33XefdOrUqdhzRkRESEBAQLmuJyMjQ5544glZunSphIWFSf/+/Ut1XK9evaR169ayZ88e2blzpzRu3FiGDx+u709LSxMvLy8ZMWKEHDhwQFavXi0ODg6yZMmSchRWRH4TkZjr6awIIMePHy/1Kd555x2ZO3euzJ07VwC5fPmyiIjk5eVJTEyM5OXlFTqmIt674ixZskTc3d1lz549IiLyxx9/iJ+fn7z44osm+WbPni3/93//J7/88oscO3ZMFixYIFZWVvLdd9+V+TkrWmXGDhXDSqbil8Yi8asIJvErTURiRJJiRGJiRGJjRbKyTPOr+FXxyhInVCWzjMocoPNF+8dviZRfumtauXKleHh4SNZNf639+/eXkSNHlu4kt7B3714B5OTJk8Xm6dixo0yePFl/bDQaxdfXV+bOnSsiWvCvU6eOrFu3Ts9z6NAhASQqKqrIc5ojSN9ozJgxpQrSCQkJAkhMTIy+bdOmTWIwGOTs2bMiIvLBBx+Iu7u7ZGdn63mmT58uzZo1ExHt89SiRQuZMGGCvv/YsWPi5OQky5YtM33CfBE5J39XLveLSLq2q6yVzAIRERGlDtLmeO9mzZolPj4+cuHCBT3Pww8/LF27dhWj0SgiIuvWrRNvb2+Jj483ef6TJ09K48aN5a233irxmh5++GEZO3ZsWV6GSlFlK5kqfomIil8iFRy/SqDHL6OI/C6SFSMS+6tWybyhDliIil8VpyzxSjWXV7RMtNG8lkgFgz1uYciQIRiNRjZs2KBvS0lJ4YcffmDcuHEA7Ny5EycnpxJTSbfy09LSMBgMuLm5Fbk/JyeH2NhYQkND9W1WVlaEhoYSFRUFQGxsLLm5uSZ5mjdvjr+/v56nqoiKisLNzY327dvr20JDQ7GysiI6OlrP88ADD2Br+/cw77CwMI4cOcLly5ext7dn1apVrFy5km+//Raj0cjIkSPp0aOH/r4A2nJqR9BWvQBwR2sed67oq9SY6737z3/+Q6NGjXj88ccBrflq9+7drFy5Ul8GbvDgwSQmJtK6dWuTMvj7+3P06FGee+65EsualpaGh4dH+S+6tlDxC1DxCyowfpVWEkgWnDBAvoCzMzQoZgnJslDxq2Kp0eUKDg4OPProoyxfvpwhQ4YA8Pnnn+Pv70/Xrl0BaN++PfHx8SWex8vLq8jtWVlZTJ8+neHDhxe5jB3AhQsXMBqNhc7h5eXF4cOHAUhKSsLW1rZQoPfy8iIpKemW11mZkpKS8PT0NNlmY2ODh4eHXtakpCQCAwNN8hRcf1JSEu7u7rRp04bXXnuNxx9/nGHDhnHy5Em+//57LbOgzX15Cq0fphXgD9SjUgf3mOu9s7a25vPPP6dNmza8+OKLLFq0iI8//hh/Mw0bXbt2LTExMSxZssQs51OqBhW/zK9S4ldZZAMXtVnYrghYWUFAgHnmxFTxq2KpSmZFcwQybpmr4p67lCZMmECHDh04e/YsDRs2ZMWKFTz22GP6pKsODg40bty4zEXIzc1l6NChiAgffvhhmY+/HU5OTvrvRqOR7Oxsk20jR45k8eLFRR4bFBTEyZMnAejSpQubNm2q2MKWwvPPP88333zDe++9x6ZNm7Tl/vKAk2jr9gLURVsa0h569+7Nzp07Tc4RFBSkv5cBAQEcPHiwEq+g9O68807efPNN/vWvf/HII4/w6KOPmuW8ERERjB07lo8++oigoCCznLNWUPFLxa9yKjJ+laDI+NU2CAMG8gFv7wD27DmIvX0FFvo2qfhVmKpkVjQDWgWgimvbti2tW7fm008/pWfPnhw8eJAffvhB379z50569+5d4jmWLFnCiBEj9McFAfrkyZNs37692LsAAPXr18fa2rrQaL3k5GS8vb0B8Pb2Jicnh9TUVJNvlDfmAUzuWERHRzN9+nQiIyP1bSWVY+PGjfpSWQVrtN4Ob29vUlJSTLbl5eVx6dIlk+sp6noL9hVISUnhjz/+wNramqNHj9IrpJc2crxgRS9fwAf97uXHH3/MtWvX9OObNGnCxo0badiwIQB1zDzXhznfO4AdO3ZgbW3NiRMnyMvLw8amfGHq559/pm/fvrzzzjuMHj26XOeqdVT8UvHrOrPFr169SnzuouLXD+9sJMezIVcBF5c6ZmkmL6DiVwWr6A6iNU1NHpn5wQcfSNOmTWXy5MnSs2dPk32ZmZly9OjRElN6erqePycnRwYMGCBBQUGSkpJSqufv2LGjPPXUU/pjo9EoDRs2LNT5+quvvtLzHD58uEp3nP/111/1bVu2bCmy43xOTo6eJzw8XO84X6B3797SrVs3+fzTz8XB3kES1iZog3t+F22AxC1QSQN/zPHerVmzRhwcHGTnzp3i4+MjL7/8cpnLffM11K1bV957771ynaeiFcSOjIwM+b//+z9p1KiR2Nvby5133imvvvqq5Of/PQomPz9fZsyYId7e3mJvby/du3eXP/74o9TPVVNjmIpft2bR+PX55+Lg4CAJCQmlL3COFr/2fnu82NHkxVHxq+Ko0eUVqKYGaBHtD8nR0VFsbW1lzZo1t32enJwc6devn9xxxx0SHx8viYmJerpxJOJDDz0k7777rv54zZo1YmdnJytWrJCEhASZOHGiuLm5SVJSkp7niSeeEH9/f9m+fbv8+uuvEhISIiEhIcWWxVxB+uDBgxIXFyd9+/aVrl27SlxcnMTFxen7o6OjpVmzZnLmzBl9W69evaRt27YSHR0tu3btkiZNmphMAZKamipeXl4yatQoOXDggKxZs0YcHR1NpgB57733xM3NTU4dPCWyX2R42HBp26ytZB/L1kZblkJZK5mJiYkSFxcnH330kQCyY8cOiYuLk5SUFD1IV8R7d/r0aXF3d5dFixaJiMjmzZvFxsam2H/At7J9+3ZxdHSU8PBwk8/gxYsXb+t8FakgdsyaNUvq1asn33//vRw/flzWrVsnTk5OsnDhQj3vvHnzxNXVVb755hvZv3+/9OvXTwIDA0sdd2pqDFPxq3gWj1+nTomIyPDhw6Vt27Ymr2OJ/tTi13fXK5kljSYvoOJXxVOVzApUUwN0gVGjRhU5HUhZHD9+XNCGpRRKERERer6AgACZOXOmybHvvvuu+Pv7i62trXTs2FGfS6zAtWvX5MknnxR3d3dxdHSUf/7zn5KYmFhsWcwVpAMCAoq8nhuf5+bK3MWLF2X48OHi5OQkLi4uMnbsWLly5YrJeffv3y+dO3cWOzs7adiwocybN0/fd+jQIXFwcJAvFn6hT010eedl8bvDT1544YVSl72slcyZM2cWea3Lli3Tg7S537v8/Hzp3r27hIWFmdy1e/rpp+Wuu+4q9LqVxpgxY4q8jgcffLDM56poBbGjd+/eMm7cOJN9AwcOlBEjRoiI9jp5e3vL/Pnz9f2pqaliZ2cnq1evLtVz1eQYpuJX0Swav774Qt92+fJl8fMrZfxKFcmP0eLXt98el8OHRfJLMa2Vil8VryxxwiAiUt4m99okPT0dV1dX0tLSCvWNycrK4vjx4wQGBmJfFXsll0L37t0JCgpi0aJFli6Kko7W9zLn+uMGaMtCWlumOEajkbi4ONq2bYu1tYUKUUMVxI5169bxySef8OOPP9K0aVP2799Pz549efvttxkxYgR//fUXd911F3FxcbRp00Y//sEHH6RNmzYsXLiw0Lmzs7PJzs7WH6enp+Pn51cjY5iKXzWEETgIiTnazGxWVhAUBHZ25Tilil9mU5Y4oQb+KABcvnyZyMhIIiMj+eCDDyxdnNotDziDtvY4gC3QCCi+v79SQ0ybNo3MzEyaN2+OtbU1RqOR2bNn6wNSCqZLKWq6leKmwZk7dy6zZs2q2IJbmIpfNcxZyMz5e21yf//yVTAVy1GVTAXQRmdevnyZ119/nWbNmlm6OLXXZbR5LwtGjnsCDbHY3Uulcn311VesWrWKL774gqCgIOLj45k6dSq+vr6MGTPmts4ZHh5uMslzwZ3MmkTFrxokA/JT4Dha+7Crq+na5Er1oiqZCgAnTpywdBFqtxy0ymXq9cf2QACVtmqPUjW89NJLhIeHM2zYMABatmzJyZMnmTt3LmPGjNGnS0lOTsbHx0c/Ljk52aT5/EZ2dnbY1fDbQCp+1RD5wAlIBK4BNjbQqJF5Jl1XLEMtK6koliRACnAQrYJpALyp1GUhlarj2rVr+hJ0BaytrcnPzwcgMDAQb29vtm3bpu9PT08nOjqakJCQSi2rophdImRkaZVM0Fb1MfO0vkolU3cyFcVSMtFW7bl6/XFdtLuXZVjpRKlZHn74YWbPno2/vz9BQUHExcXx9ttv62s9GwwGpk6dymuvvUaTJk0IDAxkxowZ+Pr6MmDAAAuXXlHKIROMiVozOWhN5O7uFi2RYgaqkqkolc2I1qO9YIEJK7R+l55U6prjStXz9ttvM3v2bJ588klSUlLw9fXlX//6Fy+//LKe54UXXuDq1atMnDiR1NRUOnfuzObNm6vlaHBFAfRm8tNoy5Tb2kIN6zZca6lKpqJUFkEb2HOavwf2uAN+aCPIlVrP2dmZBQsWsGDBgmLzGAwGXn31VV599dVKLJmiVKAkuJz594QagYFaf0yl+lNvo6JUhmtoA3uuXH9sB/gDrhYrkaIoiuVlQk6i1nMIwNsbnFV/9BqjRg38eeWVVzAYDCapefPm+v6srCwmT55MvXr1cHJyYtCgQSQnJ5dwRkUpJyPancsEtAqmAfAFglAVTEVRard8kBNwQrTpgR0dwdfX0oVSzKlGVTIBgoKCSExM1NOuXbv0fc8++yzfffcd69at4+eff+bcuXMMHDjQgqVVyuqxxx6rHgMcBK3t5wBa30tBq1Teg1bJrHF/ebXDtWvX6NKlCwaDgXfeecfSxVGqoWoTwypDEqRkaoubWRm0ZnIrFRvNJj8/nyFDhmAwGHjmmWcsUoYa93ba2Njg7e2tp/r16wOQlpbGsmXLePvtt3nooYdo164dy5cvZ/fu3ezZs6fY82VnZ5Oenm6SlOpr9uzZdOrUCUdHR9zc3Mp8/BNPPIHBYCjUZ27fvn306NEDNzc36nnUY+LQiWQkZGh9L+2BJtdTOacrfP/992nUqBH29vYEBwezd+/eEvN/9NFHdOnSBXd3d9zd3QkNDTU5Jjc3l+nTp9OyZUvq1q2Lr68vo0eP5ty5cyWc1fyysrJ47LHHaNmyJTY2NqX+J3zp0iVGjBiBi4sLbm5ujB8/noyMjHKftyh5eXkMHjyY8+fPs3DhQqZPn85nn31WKN+tXnNFKY/biWGPPfZYoVa+Xr16lfu8t+PGGNahZzCbD2p/G3f4gYND0cesW7eO5s2bY29vT8uWLdm4caPJfhHh5ZdfxsfHBwcHB0JDQzl69GiFXQPAqVOn6NOnD46Ojnh6evLvf/+bvLy8Eo/5448/6N+/P/Xr18fFxYXOnTsTERFhkicmJobu3bvj5uaGu7s7YWFh7N+//7bKOGnSJHbt2sWSJUv45JNPeO211wrl+frrr+nRowcNGjTAxcWFkJAQtmzZclvPV5QaV8k8evQovr6+3HnnnYwYMYJTp04BEBsbS25uLqGhoXre5s2b4+/vT1RUVLHnmzt3Lq6urnqqaStlWEJOTs6tM1Xgcw8ZMoRJkyaV+dj169ezZ88efG9qzzl37hyhoaE0DmxM9LpoNr+zmcoqW4AAACAASURBVIN/HOSxVx/T1hpvQaGm8cjISBo1alSm5//yyy957rnnmDlzJvv27aN169aEhYWRkpJS7DGRkZEMHz6ciIgIoqKi8PPzo2fPnpw9exaAzMxM9u3bx4wZM9i3bx9ff/01R44coV+/fmUq280aNWpEZGRkqfMbjUYcHByYMmWKyd/orYwYMYKDBw+ydetWvv/+e3bs2MHEiRPLfd6biQiPPfYYZ8+eZceOHUyZMoV169YxadIkfvjhB5O8t3rNleqvOsawXr16mbTyrV69ulznLVcMmzGTmLX7CGjSmqefDiMvL4UGDYo+Zvfu3QwfPpzx48cTFxfHgAEDGDBgAAcOHNDzvPHGGyxatIjFixcTHR1N3bp1CQsLIysrq0zlu1FJMcxoNNKnTx9ycnLYvXs3K1euZMWKFSazQBTlH//4B3l5eWzfvp3Y2Fhat27NP/7xD31J2IyMDHr16oW/vz/R0dHs2rULZ2dnwsLCyM3NLfHcN3vppZfYvHmzHhO3bt3K22+/zZIlS0zy7dixgx49erBx40ZiY2Pp1q0bffv2JS4urkzPVyypQTZu3Chr166V/fv3y+bNmyUkJET8/f0lPT1dVq1aJba2toWO6dChg7zwwgvFnjMrK0vS0tL0dPr0aQEkLS2tUN5r165JQkKCXLt2Td+Wny+SkWGZlJ9futdt5cqV4uHhIVlZWSbb+/fvLyNHjizx2JkzZ0rr1q1l8eLFcscdd4iDg4MMGTJEUlNT9TxjxoyR/v37y2uvvSY+Pj7SqFEjERE5deqUDBkyRFxdXcXd3V369esnx48f14/Ly8uTZ599VlxdXcXDw0P+/e9/y+jRo6V///6lu7ASLF++XFxdXUud/8yZM9KwYUM5cOCABAQEyDvvvKPvW/LBEvGs7ynGvUaRGBGJEflt028CyNGjR4s8X0REhAQEBJSpzB07dpTJkyfrj41Go/j6+srcuXNLfY68vDxxdnaWlStXFptn7969AsjJkydFRPt81K1bVw4dOiQxMTGSl5cnkyZNkmbNmsnVq1eLPEdAQIBERESUulw3Kvi83EpCQoIAEhMTo2/btGmTGAwGOXv2bKnOm5+fL927d5eePXtK/vU/mIsXL0rDhg1lxowZer4pU6ZIcHCwXLp0yeT4H3/8UerXry87d+4stpylec2Lih0VJS0trdQxrDrELxEVw26ltH9TZTlvuWLYGZETMSLR0UZp0MBXXnut+Bg2dOhQ6dOnj8m24OBg+de//iUi2t+wt7e3zJ8/X9+fmpoqdnZ2snr1ahH5O4b973//k7y8PBGRcsWwjRs3ipWVlSQlJenbPvzwQ3FxcZHs7Owijzl//rwAsmPHDn1benq6ALJ161YREYmJiRFATp06pef57TfT/yVjx46Vli1b6p/17OxsadOmjYwaNUo/5u2335bGjRvrMbxAXFyceHt7y7p164osY4EWLVrIrFmzit1flnhVo+5k9u7dmyFDhtCqVSvCwsLYuHEjqamprF279rbPaWdnh4uLi0kqi8xMcHKyTMrMLF0ZhwwZgtFoZMOGDfq2lJQUfvjhB30S6JIcO3aMtWvX8t1337F582bi4uJ48sknTfJs27aNI0eO6HeccnNzCQsLw9nZmZ07d/LLL7/g5OREr1699LsEb731FitWrOCTTz5h165dXLp0ifXr15ucd86cOTg5OZWYCu5m3678/HxGjRrFv//9b4KCgm7YASRD9olsbK1ssTJYgQvQAhwaa+0+N/YJLo+cnBxiY2NN7sZZWVkRGhpa4p34m2VmZpKbm4uHh0exedLS0jAYDHqT2ejRo3n44YcZNWoUeXl5/PDDD3z88cesWrUKR0fLzRwfFRWFm5sb7du317eFhoZiZWVFdHR0qc5hMBhYuXIlMTExLFq0CNC6RDRs2NDkrsTChQvZs2cP7jfNDt2jRw/Onz9P586di32O0rzmVVV1iF+gYlhpREZG4unpSbNmzZg0aRIXL14s9znLQo9hnUO5nAjn+TuG7d1bfAyLiooq1AoRFhamx73jx4+TlJRkksfV1ZXg4GA9z+jRo+nduzczZswwSwyLioqiZcuWeHl5mZQpPT2dgwcPFnlMvXr1aNasGZ9++ilXr14lLy+PJUuW4OnpSbt27QBo1qwZ9erVY9myZeTk5HDt2jWWLVvG3Xffrd81XrRoEVevXuXFF18E4D//+Q+pqam89957+nM9++yzHD16FH9/f5MytGnThsTERAYPHlzsteXn53PlyhWzxasaPYWRm5sbTZs25dixY/To0YOcnBxSU1NN+pskJyfr6wHXVg4ODjz66KMsX76cIUOGAPD555/j7+9P165db3l8VlYWn376KQ0bNgTg3XffpU+fPrz11lv6a1u3bl0+/vhjbG1t9fPn5+fz8ccfY7i+MO3y5ctxc3MjMjKSnj17smDBAsLDw/XBWYsXLy7UV+SJJ55g6NChJZbv5ubtsnr99dexsbFhypQpf2+8ijaoJwceuvchnnv7OeZvms8zLzzD1cy/A0BiYmKR5yyrCxcuYDQaTYIagJeXF4cPHy71eaZPn46vr2+xTcdZWVlMnz6d4cOHm3yhWrJkCa1ateLNN99k165dvPLKK3pgtJSkpCQ8PT1NttnY2ODh4aE3P5VGw4YNWbJkCaNHjyYpKYmNGzcSFxeHjZkm6rvVa66Un4phJevVqxcDBw4kMDCQP//8k5deeonevXsTFRWFtbV1uc5dWgUxzD3PixPXt3l7wx13ePHzz8XHsKSkpCLjXsHfeMHPkvIAfPjhhwQFBTF16lTWr19frhhWXJluLM/NDAYDP/30EwMGDMDZ2RkrKys8PT3ZvHmz/uXV2dmZyMhIBgwYwH//+18AmjRpwpYtW/R45OTkxOeff86DDz6oz6sbERFR5htgxXnzzTfJyMi45WeytGp0JTMjI4M///yTUaNG0a5dO+rUqcO2bdsYNGgQAEeOHOHUqVMVuuavoyPcMA6hUpXlC9qECRPo0KEDZ8+epWHDhqxYsULvLH4r/v7+enAGCAkJIT8/nyNHjugBumXLlnpwBti/fz/Hjh3D+aYJ0bKysvjzzz9JS0sjMTGR4OBgfZ+NjQ3t27dHRPRtHh4eFXqHKDY2loULF7Jv3z4MGLT1xXOBi0AOUAeCHgpi5YqVPPf8c4TPCsfa2popU6bg5eVlsg61k5OT/rvRaCQ7O9tk28iRI1m8eDE7d+6kd+/e+vYlS5bQrVu3cl/LvHnzWLNmDZGRkUWuDpObm8vQoUMRET788EOTfe7u7ixdupSHH36YkJAQvRJd4IknnuDzzz/XH2dmZtK7d2+Tf2AFA3KCgoI4eVKbFa9Lly5s2rSp3NdWXkOGDGH9+vXMmzePDz/8kCZNmpjlvLd6zau66hK/QMWwkgwbNkz/vWXLlrRq1Yq77rqLyMhIunfvXurzmCOGncvRVtCtW8nTFbm7uzNjxgyefvppOnXqVK4YdjtEhMmTJ+Pp6cnOnTtxcHDg448/pm/fvsTExODj48O1a9cYP348999/P6tXr8ZoNPLmm2/Sp08fYmJicLg+MiokJIRp06bx3//+l+nTp5fYklIWX3zxBbNmzeLbb78t9AX+dtWoSua0adPo27cvAQEBnDt3jpkzZ2Jtbc3w4cNxdXVl/PjxPPfcc3h4eODi4sLTTz9NSEgI9913X4WVyWCAunUr7PRm07ZtW1q3bs2nn35Kz549OXjwYKEBDeVR96YXISMjg3bt2rFq1apCeRsU1wO8CHPmzGHOnDkl5klISCjUbFBaO3fuJCUlxeR4o9HI8wufZ8G6BZw4cQKs4dERj/LoiEdJTk6mbt26GAwG3n77be688079uPj4eP336Ohopk+fbtKxvOCbaPv27U3yenl5YWdnh7W1daF5XUt7J/7NN99k3rx5/PTTT7Rq1arQ/oIK5smTJ9m+fXuR34p37tyJtbU1SUlJXL161eSf66uvvsq0adP0x127duX11183+QdbYOPGjXondofihpOWgre3d6FBT3l5eVy6dKnMrROZmZnExsZibW1ttlGpt3rNq4PqEr9AxbCyuPPOO6lfvz7Hjh0rUyWzXDEsW4thZy8l09wK7rxLm67oVjHM29u7xLhX8DM5ORkfHx+TPG3atDE5Li4uDmtraxITE8sVw7y9vQvNGFFQxuKuZfv27Xz//fdcvnxZf50++OADtm7dysqVK3nxxRf54osvOHHiBFFRUfoNii+++AJ3d3e+/fZb/ctCfn4+v/zyC9bW1hw7dqy4l65M1qxZw+OPP866devM2upSoyqZZ86cYfjw4Vy8eJEGDRrQuXNn9uzZo//Bv/POO1hZWTFo0CCys7MJCwvjgw8+sHCpq47HH3+cBQsWcPbsWUJDQ0s9kv7UqVOcO3dOb9LZs2cPVlZWNGvWrNhj7r33Xr788ks8PT2Lvc3v4+NDdHQ0DzzwAKBVIGJjY7n33nv1PBXd1DTqn6MIvStUax4HsIKwKWGMGj2KsePHwk0tTQVNJp988gn29vb06NFD39e4cWP99zNnzmBjY2OyrYCDg0OR29u1a8e2bdv0aXjy8/PZtm0bTz31VInX8MYbbzB79my2bNli0n+xQEEF8+jRo0RERFCvXr1CeXbv3s38+fN56623WLZsGU899RQrV67U93t6epp887WxsaFhw4ZFXkdAQECJ5S2tkJAQUlNTiY2N1Zu9tm/fTn5+fpH/GEry/PPPY2VlxaZNm3j44Yfp06cPDz300G2X7VavuVIxVAwrnTNnznDx4kWTSllp3HYMy4P0P6F583bExGxj3LgB2NmVLoaFhISwbds2pk6dqm/bunWr3gIZGBiIt7c327Zt0yuV6enpREdHm4yULxgF/s033/DSSy+VK4aFhIQwe/ZsUlJS9GO2bt2Ki4sLLVq0KPI6Mq93Mra6aSJQKysr8vPz9TxWVlYmd98LHhfkAZg/fz6HDx/m559/JiwsjOXLlzN27NhiX8NbWb16NePGjWPNmjX06dPnts9TpFsODVJMlGVkZnWTmpoqjo6OYmtrK2vWrCnVMTNnzpS6detKaGioxMfHy44dO6Rp06YybNgwPU9RIxuvXr0qTZo0ka5du8qOHTvkr7/+koiICHn66afl9OnTIiIyb9488fDwkPXr18uhQ4dkwoQJ4uzsXK6RmSdPnpS4uDiZNWuWODk5SVxcnMTFxcmVK1f0PM2aNZOvV30tckT00eLyq4icFJFsKTS6XETk3XffldjYWDly5Ii899574uDgIAsXLiy2HLczMnPNmjViZ2cnK1askISEBJk4caK4ubmZjHAcNWqUvPjii/rjefPmia2trXz11VeSmJiop4LrzcnJkX79+skdd9wh8fHxJnkKRkmmp6fLnXfeKVOnTpWYmBiJi4sTOzu7Ekco3s7o8oMHD0pcXJz07dtXunbtqr83BaKjo6VZs2Zy5swZfVuvXr2kbdu2Eh0dLbt27ZImTZrI8OHDy3Te77//XmxtbSU2NlZERMLDw+WOO+4oNJK8tG71mhelqo4ur25UDNM0a9ZMvv76axERuXLlikybNk2ioqLk+PHj8tNPP8m9994rTZo0MRmNX5rz3qjUMSxfJOcPkbgYkdmz14itbdli2C+//CI2Njby5ptvyqFDh2TmzJlSp04d+f333/U88+bNEzc3N/n222/lt99+k/79+0tgYKD+OS6IYY8++qjk5eXJb7/9Vq4YlpeXJ/fcc4/07NlT4uPjZfPmzdKgQQMJDw/X89wcr86fPy/16tWTgQMHSnx8vBw5ckSmTZsmderUkfj4eBEROXTokNjZ2cmkSZMkISFBDhw4ICNHjhRXV1c5d+6ciIjs27dPbG1tZcOGDSIismTJEnF2dpY///zz1u9FEVatWiU2Njby/vvvm8SrG2dXuFlZ4oSqZJZRTQ7QItofeFFTgRSnYPqPDz74QHx9fcXe3l4GDx5s8g+6uOkzEhMTZfTo0VK/fn2xs7OTO++8UyZMmKC/trm5ufLMM8+Ii4uLuLm5yXPPPVfu6T/GjBkjaOvvmCQ9mKSLALL85eV/Vy6Pi8gNL0dRlcyC183W1lZatWoln376aYnluJ1KpohWmfX39xdbW1vp2LGj7Nmzx2T/gw8+KGPGjDEpa1HXO3PmTBEROX78eJH7b3xNCqbMuHr1qj6F0VtvvSUeHh4mFb4b3U4ls7iyFoiIiBDAZIqYixcvyvDhw8XJyUlcXFxk7Nixhf4plnTelJQU8fLykjlz5uj5c3JypF27djJ06NAylf9Wz1fwmhdFVTLNp9bHMLkew5YvFxGRzMxM6dmzpzRo0EDq1KkjAQEBMmHCBJOKXWnPe6PSxrD88yKHY0RiYkQO/CayaFHZYpiIyNq1a6Vp06Zia2srQUFB8sMPP5g+R36+zJgxQ7y8vMTOzk66d+8uR44c0fcXxLBffvlFn8KovDHsxIkT0rt3b3FwcJD69evL888/L7m5uSavz83xKiYmRnr27CkeHh7i7Ows9913n2zcuNHkvD/++KPcf//9+rRYDz30kERFRYmI9vfZokULmThxoskx/fr1k06dOunXVhYPPvhgke/7ze/BjcoSJwwiN/RAVm4pPT0dV1dX0tLSCjWRZGVlcfz4cQIDA6tlJ3+A7t27ExQUpE/nciuvvPIK33zzjUn/m2pH0NYVT7z+E7Q1xusBPpR7lZ6awmg0EhcXR9u2bSttRGptUZmxQ8UwUzUihlVV2XDuAJwTbdnIu1sUv6pPRVPxy3zKEidqVJ9M5fZdvnyZyMhIIiMja08/VUEbLZ7E330uDUB9wBtVuVSUaqRWxrCqTCD9mFbBBAgIsFwFU7EcVclUAG1k5uXLl3n99ddNOrvfON3MzW5enqrayEebgigZKFh1zIq/K5e2xRynKEqVVatiWDWQcwb+uqb9Xt8d6tW3bHkUy1CVTAVAm4qnCDdON3MzLy8vnJ2deeWVVyquYOaUB6SgLTVRcEnWgOf1VMdC5VIUpdxqRQyrJuQK/JWshVwHW/APtHSJFEtRlUylROaabsairqFVLi+i3cUE7W6lJ9CAQtMQKYpSc9SIGFad5MHZY5CB1g/zrqbafJhK7aQqmRXgxvmsFAsRIA2tcpl+w3ZHwAtwR2siV5QqoKrFjKpWHqWaELh8DJKM2sNGAVBNx48pJShLfFCVTDOytbXFysqKc+fO0aBBA2xtbUu1pJliRnnA5esp54btzmh9Lh3RBvfkFD5UKZnRqP3nyMrKUqMzzUREyMnJ4fz581hZWZksW2gJKoYp5ZGdAsevr7xYzxUcnSArq+RjKouKX+V3O/FKVTLNyMrKisDAQBITEzl37pyli1O7ZKNNP5SJdhcTtDuVTmgVzHy0u5rKbcvPz+fChQucOHGi0KoVSvk4Ojri7++PlZUVZ8+eZfr06WzatInMzEwaN27M8uXL9ZWDRISZM2fy0UcfkZqayv3332+29dZVDFNuV34OJCVq3d3tbLS1548ft3Sp/qbil/ncGK9uRVUyzczW1hZ/f3/y8vL0b05KBUkFvgPWAX/csP1uYDjwD7Q7l4pZZGRk0KdPH3799VecnJwsXZwaw9raGhsbGwwGA5cvX+b++++nW7dubNq0iQYNGnD06FHc3d31/G+88QaLFi1i5cqVBAYGMmPGDMLCwkhISDDL3JYqhillJdfghQfhu3RoYAv/2wqeXpYulSkVv8zjxnhVGmoy9jIqaSJjpRIYge3AJ8B6tDuYAPbAI8C/gPvQmsQVs1Kf/Yr34osv8ssvv7Bz584i94sIvr6+PP/880ybNg2AtLQ0vLy8WLFiBcOGDSt0THZ2NtnZ2frj9PR0/Pz81PuomM2i++GZ3doYyoj10GWApUtUmIpflqHuGSvVwyHgJaAR0BNYg1bBbA28C5wDVgAhqAqmUm1t2LCB9u3bM2TIEDw9PWnbti0fffSRvv/48eMkJSURGhqqb3N1dSU4OJioqKgizzl37lxcXV315OfnV+HXodQeO2bC87u139+aVDUrmIrlqEqmUnUlAu8A7YEWwFzgDOAGPAn8CsQBT6GNFleUau6vv/7S+1du2bKFSZMmMWXKFFauXAlAUlISoM3veCMvLy99383Cw8NJS0vT0+nTpyv2IpRa4/TPMOS/2njLEUEw5X1Ll0ipalSfTKVquYDWDL4GiODvQTw2QC9gNNAXrXlcUWqY/Px82rdvz5w5cwBtFZsDBw6wePFixowZc1vntLOzw85OrZGqmFfWZRjYG1IE2tSFpbtBTUSg3EzdyVQsLxlYitYM7g1MROt3KWjN3++hNYd/BwxBVTCVGsvHx4cWLVqYbLv77rs5deoUAN7e3gAkJyeb5ElOTtb3KUpFE4F/BcOv16CeAdZvA0fVzVEpgrqTqVjGn8C3wDfALv6+YwnQFm0QzyNofTAVpZa4//77OXLkiMm2P/74Q1+1JjAwEG9vb7Zt20abNm0AbUBDdHQ0kyZNqvTyKrXTwpHw6VFtoM+X86BRsKVLpFRVqpKpVI48IAr4Ae2OZMJN+9sDg4DBQOPKLZqiVBXPPvssnTp1Ys6cOQwdOpS9e/eydOlSli5dCoDBYGDq1Km89tprNGnSRJ/CyNfXlwED1IgLpeJtXQrPf6H9/lYv6P6CZcujVG2qkqlUnDPAj8BmYCvavJYFbIAHgAFAf8C/0kunKFVOhw4dWL9+PeHh4bz66qsEBgayYMECRowYoed54YUXuHr1KhMnTiQ1NZXOnTuzefNms8yRqSglOboPhk7S1rZ4zBemfGfpEilVnZons4zUXFsluAz8DGy7ng7dtN8DbfDOP67/VCPCqxX12a8Z1Puo3I7UyxDiD4czIMQWIv4Cu4aWLlXpqc+9Zag7mcrtO4/Wn3IHWuUyHtO+lVZAB7QKZRjQEa0Tj6IoilJt5OXBsPu0CmZD4OtvqlcFU7EcVclUSicPrR/lHrS+lbsxXcqxQHOgGxB6/ae6W6koilKtTXsEtvwBDsCGl8C7t6VLpFQXqpKpFGZEq0DuA2LRJj3fB1wtIu89QGfgQbQ+lr6VVEZFURSlwn34Giz8Wvv9025w72uWLY9SvahKZm0maKvqJAAHgN+vpwPAtSLyO6M1f4fckDwqpaSKoihKJdv6PTw9Q/t9ti8M/gG1bK9SJqqSWdMJcBH4C21uyqPX0x/AYSC9mOPqoq0Lfi9axbI90AzVp1JRFKUWOHgABg/UGrZG2UH4brT2ckUpg1pbyXz//feZP38+SUlJtG7dmnfffZeOHTtaulhlk4U2+Cb5ekoEzl5Pp4FTwEmKbuYuYAXchdbsHYRWsWyFNlelWg9KURSl1klOhn88AOm50AX4aAMYAixdKqU6qpWVzC+//JLnnnuOxYsXExwczIIFCwgLC+PIkSN4enqW69y5l+HYv8HaAWwcoI4j2DqCvSPYO4CtHRis0Zoc5HrKu55ygRy0yuM1IBPIAK6g3XFMQ5sm6NL1lFGGgvmiVRzvAppcT3df36aWNVYURVGAzEzo+wCcuKz9u/h6Dtj1tHSplOqqVs6TGRwcTIcOHXjvvfcAyM/Px8/Pj6effpoXX3yxxGNvNdfWmb3gV8ISW1ZoLdFOaF0cXQG366keUP968gS8AB+0+qELxXSFsbme2fuGzA0Bv+spAG2iczVPs1JOap65mkG9j0pxjEYY0hvWb9X+H0UNhCZfUSP6YarPvWXUujuZOTk5xMbGEh4erm+zsrIiNDSUqKioQvmzs7PJzs7WH6enF9eJ8ToH8LAHYz7kXU/Z+X/vzke7MXkFrXW7tBxtwa8++HlCgD8EBELg3XDnPdC4CTRoAIYaEAgURVGUyicCz03WKpi2wDdB0OQLakQFU7GcWlfJvHDhAkajES8vL5PtXl5eHD58uFD+uXPnMmvWrFKf/46WcPGmkdkikJurNUMUpCtXtJSWBqmpcOmSli5cgPPntZSUpKXUVMjMgSPntER84ed1doamTaF5cy3dfTcEBUHjxmBT695lRVEUpSzeeRMWLdF+/8wDOv+E6kqllFuZqx9jxoxh/PjxPPDAAxVRnionPDyc5557Tn+cnp6On59fmc5hMICtrZbc3MpehsxMOHcOTp+GU6e0dPy4lv78E86c0SqssbFaupGtLbRoAa1bQ5s2WmrbFlxdy14ORVEKq20xUal51qyB51/Qfp9fB4b+hNYFS1HKqcyVzLS0NEJDQwkICGDs2LGMGTOGhg2rz/pS9evXx9ramuTkZJPtycnJeHsX/quys7PDzs6yX+ccHbU7ko0bF70/Kwv++guOHNHSoUOQkKD9vHoV4uO1tHLl38c0aQLt20OHDnDffVrF017121SUMqvuMVGp3bZvh9Ejtd+fAZ7/AmhryRIpNcltDfw5f/48n332GStXriQhIYHQ0FDGjx9P//79qVOnTkWU06yCg4Pp2LEj7777LqAN/PH39+epp54q98CfqiQ/H06cgN9+g/37tbRvH5w8WTivra1W0bz/fi116aL181SUAtXps1/ZqlNMVO+jUiA+Hh64H65kwhBgzWtg9R9Ll6piqM+9ZZR7dPm+fftYvnw5H3/8MU5OTowcOZInn3ySJk2amKuMZvfll18yZswYlixZQseOHVmwYAFr167l8OHDhfpq3qwmfFAvXtSa1WNiIDoa9uzR+oDerEULePBB6NYNunZVlc7ariZ89itDVY+J6n1UQGv9uj8Yki5AV2DTCLD/jBo70Ed97i2jXENCEhMT2bp1K1u3bsXa2pqHH36Y33//nRYtWvDGG2/w7LPPmqucZvXII49w/vx5Xn75ZZKSkmjTpg2bN2++ZQWzpqhXD3r21BJoA5OOH4fdu+GXX2DXLjhwQGtyT0iADz/U8rVuDaGh2nFduoCDWv1BUUxU15io1C5JSdCzu1bBbAV80wnsl1FjK5iKd36xKAAAIABJREFU5ZT5TmZubi4bNmxg+fLl/Pjjj7Rq1YrHH3+cRx99VP92sH79esaNG8fly5crpNCWVFu+DV28CDt3QkSEln7/3XS/vb12d/Phh7V0110WKaZSiWrLZ7+sqltMVO9j7ZaaCt0ehPjfIBD4JRB8YtAmxqzB1OfeMsp8J9PHx4f8/HyGDx/O3r17adOmTaE83bp1w+12hlErVUa9ejBggJYAUlJg2zb46SfYsgXOnoXNm7U0ZYo2bdI//gH9+0NICFirNc6VWkLFRKW6yMyEvv/QKpiewI/u4LOVGl/BVCynzHcyP/vsM4YMGYJ9LR2KrL4Nac3rCQmwaRP88IPWvJ6X9/f+Bg2gXz8YOBC6dwcLD85XzER99otW3WKieh9rp5wc7abBpk3aSnM/20LrSCDEwgWrJOpzbxm1clnJ8lAf1MJSU7W7m999p1U6U1P/3ufiolU4hw7V+nKqCmf1pT77NYN6H2sfoxGGD4d168AB2Arc/zXwTwsXrBKpz71lWFm6AEr15+YGjzwCn3+uNav/9BM8+ST4+EB6ura9Xz/w8oJx4+DHH03vfCqKUti8efMwGAxMnTpV35aVlcXkyZOpV68eTk5ODBo0qNCcv4pyo/x8ePxxrYJpC3wD3L+IWlXBVCxHVTIVs6pTR2sif/99bSWiXbvgmWfA11dbQnP5cggLgzvugGef1ebtVPfSFcVUTEwMS5YsoVWrVibbn332Wb777jvWrVvHzz//zLlz5xg4cKCFSqlUdSLw9NOwYgVYA6uBntOBpy1bLqX2UJVMpcJYWWkTuy9YoC2J+fPP8MQT2qCi5GRte7t20LIlzJ8PiYmWLrGiWF5GRgYjRozgo48+wt3dXd+elpbGsmXLePvtt3nooYdo164dy5cvZ/fu3ezZs8eCJVaqIhF4/nn44ANtZqJPgYGjgLkWLphSq6hKplIprKzggQe0OTfPndP6bz7yiNZH8+BBeOEF8PPTmtW//RZycy1dYkWxjMmTJ9OnTx9CQ0NNtsfGxpKbm2uyvXnz5vj7+xMVFVXs+bKzs0lPTzdJSs0mAi+9BO+8oz1eCjz6MKDmwlQqmapkKpXO1lab7mjNGu2O5tKl2rRHRqNW+RwwAPz94T//0SaJV5TaYs2aNezbt4+5cwvfbkpKSsLW1rbQVEheXl4kJSUVe865c+fi6uqqJz8/P7OXW6laZs6EefO0398HHg8B1gFVa4VTpRZQlUzFolxdYcIEbbWhQ4fg3//WpkBKSoI5c7RJ3nv3hg0btEqootRUp0+f5plnnmHVqlVmnQ4pPDyctLQ0PZ0+fdps51aqnlmz4L//1X5/B3iyJfAD4GjBQim1lqpkKlVG8+bwxhvagKGvvoIePbRmn82btUne77pL+3Z+4YKlS6oo5hcbG0tKSgr33nsvNjY22NjY8PPPP7No0SJsbGzw8vIiJyeH1BvnCAOSk5Px9vYu9rx2dna4uLiYJKVmeuUVLQHMB6beCWwB3Is9RFEqlKpkKlWOrS0MGqRNdXTsmHZ308MDTp6E8HBtZPq4cbB/v6VLqijm0717d37//Xfi4/+fvTsPr+laHzj+PYnMkcSQkSQoglBDSRpV1WsIVcMtWqqmahWhV9XYXkMHtHQw1tBqaY3V6mSsIYrKjzSCmukNSclASUJkzvr9seXUaQYJJ3aG9/M855Gz99r7vPuc482bvfda64jx0bJlS/r372/82crKil27dhm3OXPmDNHR0QQFVZARtUW+lIKpU7WzmACzgXE1gJ2Ap46BiQpPikxRqj300N9nN7/4QuuNnp6u/dysmTZc0qZN2lhwQpRllStXpnHjxiYPBwcHqlWrRuPGjXF2dmbo0KGMHTuW0NBQIiIiGDJkCEFBQTz66KN6hy90ktvJJ/cS+RxgvCvaiOu1dQxMCKTIFGWEnR0MHgzh4fDrr9CnjzY/+u7d0K0b+PvDp59CWprekQpRcj7++GOefvppevXqRdu2bfHw8GDjxo16hyV0kjtMUW4nn4+BcS5oBWZDHQMT4jaZVrKYZGqq0iM6GhYs0Hqn547K4u6uDf4+YoQ2E5EwH/nulw/yOZYPOTkwapQ2LBzAQiDECa3ADNAxsFJKvvf6kDOZoszy8dEGcY+JgQ8/1MbZjI/XLh35+MCkSdpzIYQoT7KyYMgQrcA0AJ8BIY7AVqTAFKWKFJmizHNygrFj4Y8/4MsvtUvnN27A++9DrVrw6qvaPZ1CCFHWpadrE1l8+SVYGmAVMNQB2AK01jk4If5BikxRblhZwYABcOyYNmtQYKB2j+aCBVoHohEjtB7qQghRFqWkaPegb9wI1gb4VsHz9mgF5uN6RydEXlJkinLHwkKbnjIsDHbuhCeegIwMWLIE6tXT5k+PjtY7SiGEKLq//tJG09ixAxwsYYuCHg7ANqCt3tEJkT8pMkW5ZTBoSXnPHvjlF+3nzExYulQrNkeN0uZRF0KI0iwmBtq2hYMHoWol2JUN7SujFZhyBlOUYlJkigqhbVvtrObevfDkk9qZzUWLtMvo48drZwmEEKK0OXkSWrfW/q1hBfuyINAZrRd5G72jE6JwUmSKCuXxx7WxNXfv1hJ3Whp88AHUqQPvvqvd8ySEEKXBvn3w2GNax8WGNnAgExpVA3YBgXpHJ8TdSZEpKqQnn4T9+2HzZm3moORkmDJFO7O5eLF2WV0IIfTyzTfQsSMkJkKQLexLBx8PYA/wiM7BCVFEUmSKCstggKeegogIWLtWKzDj42HkSGjcGL77TptRQwghHhSltHF/+/TRhivqaQu70qBaLWAf0FjnAIUoBikyRYVnYQF9+2r3PC1cCK6ucPYsPPOM1jM9PFzvCIUQFUFWFoSEwLhx2vNRNvBNGtg1BPYDdfWMTojikyJTiNusrbUEf/48/Pe/2nzp+/ZBQAC88ILWw1MIIUpCUpI2BubixdpVlg8rwfx0sAxEO4NZQ+8IhSi+clVk1qpVC4PBYPJ47733TNocO3aMxx9/HFtbW7y9vZk9e7ZO0YrSyskJ3nlHO5s5aJCW8FevBj8/mD4dbt3SO0IhRHkSFaV18Nm2DeysYaMBxmaBoTOwE6imd4RC3JtyVWQCvP3228TGxhofo0ePNq5LTk6mU6dO+Pr6EhERwZw5c5g+fTrLli3TMWJRWtWsCStWaJfLH38cUlPhrbegQQNYv17u1xRC3L+9e7WrJSdOgFdl2JsBPXOAgcCPgKPOAQpxH8pdkVm5cmU8PDyMDwcHB+O61atXk5GRweeff46/vz99+/bl1Vdf5aOPPtIxYlHaPfKINpj711+Dj4922bxvX62H+u+/6x2dEKKs+vRTbZKIq1ehRVU4dANaAvwXWAFY6RqeEPet3BWZ7733HtWqVaN58+bMmTOHrKws47qwsDDatm2LtbW1cVlwcDBnzpzh+vXr+e4vPT2d5ORkk4eoeAwGrbfn6dPa2Uw7O63wbN4cXntNu59KCCGKIiMDRoyAYcO0zj7PusK+a1DDElgGvAMYdA5SCDMoV0Xmq6++yrp16wgNDeWVV15h5syZTJgwwbg+Li4Od3d3k21yn8fFxeW7z1mzZuHs7Gx8eHt7l9wBiFLPzg6mToVTp6BXL8jOhrlztUvoa9bIJXQhROFiY+Ff/4IlS7Q/XmdUg3VXwL4ysBl4We8IhTCfUl9kTpo0KU9nnn8+Tp8+DcDYsWNp164dDz/8MMOHD+fDDz9kwYIFpKen3/PrT548maSkJOMjRroYC8DXVxsseft2qF8f4uKgf3/t0teZM3pHJ4Qojfbv126/+fVXcHaAn+zhjb/A4AMcAIL1jlAI86qkdwB38/rrrzN48OBC29SpUyff5YGBgWRlZXHhwgX8/Pzw8PAgPj7epE3ucw8Pj3z3YWNjg42NTfEDFxVCp05w7Jg2NeW770JoKDz8MEyaBJMng62t3hEKIfSmFMybB+PHa5fH/T3guwSolwM8CnwH5P8rSIgyrdQXma6urri6ut7TtkeOHMHCwgI3NzcAgoKCePPNN8nMzMTKSrujeseOHfj5+VGlShWzxSwqFhsbePNN6NcPRo2CrVvh7bdh3TpYuhTatdM7QiGEXpKSYOhQ+PZb7Xm/OrDsf7c7jQ9AuwdT/hgV5VSpv1xeVGFhYcydO5ejR4/yv//9j9WrV/Paa6/xwgsvGAvI559/Hmtra4YOHcqJEydYv3498+bNY+zYsTpHL8qDOnW0udA3bABPT22czSef1H7BFNCvTAhRjkVEaJfHv/0WrKxgvg+s/h84WgAfASuRAlOUa+WmyLSxsWHdunU88cQT+Pv7M2PGDF577TWTMTCdnZ35+eefiYqK4pFHHuH1119n6tSpDBs2TMfIRXliMEDv3lrHoBEjtGWffw4NG/59JkOIgsyaNYtWrVpRuXJl3Nzc6NmzJ2f+cZNvWloaISEhVKtWDUdHR3r16pXnNiChr9zL461bwx9/gK877LOH0dFgqApsA15DepCLcs+glPSHLY7k5GScnZ1JSkrCyclJ73BEKbd/P7z8sjb0EWjzoS9aBAXcAlyqyXe/5HXu3Jm+ffvSqlUrsrKyeOONNzh+/DgnT540jvk7YsQINm/ezIoVK3B2dmbUqFFYWFjw66+/Fuk15HMsWVeuwIsvwqZN2vOeDeHz01BFAc2AjUBtHQOsoOR7rw8pMotJvqiiuNLTYcYMmDVLu+m/ShVt2KMBA7Qzn2WFfPcfvCtXruDm5sYvv/xC27ZtSUpKwtXVlTVr1tC7d28ATp8+TcOGDQkLC+PRRx/Ns4/09HSTETaSk5Px9vaWz7EEbN8Ogwdro03Y2MCHdWDkqdsnLF8EFgJ2uoZYYUn+0ke5uVwuRGllY6N1BPrtN2jRQrs/c9Ag6N4dLl/WOzpRmiXdHuW/atWqAERERJCZmUmHDh2MbRo0aICPjw9hYWH57kPG+i15qanw6qvQubNWYDbyhYNOEHIKDHbA58BypMAUFY4UmUI8IE2bwv/9n3ZW09pau5zm7w+rVskg7iKvnJwcxowZw2OPPUbjxo0BbdIIa2trXFxcTNq6u7sXOKGEjPVbsg4d0mb+WrBAex7SEn67CE2vAA2Ag8AQHQMUQkdSZArxAFlZwRtv/N3rNDFRu2zeqxckJOgdnShNQkJCOH78OOvWrbuv/djY2ODk5GTyEPcvPV0buqx1a20CBk832NoAFv52+4TlEOA3oIm+cQqhJykyhdBB48YQFgbvvKMVnt99py374Qe9IxOlwahRo9i0aROhoaHUrFnTuNzDw4OMjAwSExNN2sfHxxc4oYQwv0OHtD8SZ87UppbtFwDHb0Ln04ATsA7tErmDvnEKoTcpMoXQiZUV/Pe/2i+sxo21Xqk9e2o9U5OT9Y5O6EEpxahRo/juu+/YvXs3tWubdkN+5JFHsLKyYteuXcZlZ86cITo6mqCgoAcdboWTkgLjxkFQEJw4AW7V4duWsOYQVL0FtAWOAc/pHKgQpYQUmULorFkzrVPQhAlab/MvvtCWFXFEGlGOhISEsGrVKtasWUPlypWJi4sjLi6O1NRUQBvrd+jQoYwdO5bQ0FAiIiIYMmQIQUFB+fYsF+azbZv2x+CHH0JODvRvDScy4ZnfAGtgDrAb8NU3TiFKEykyhSgFbGzg/fdhzx7w9YWoKGjbFqZOhcxMvaMTD8rixYtJSkqiXbt2eHp6Gh/r1683tvn44495+umn6dWrF23btsXDw4ONGzfqGHX5dukSPPccdOkCFy6ATw3Y3ApWHYDqSUALIAIYB1jqGqoQpY6Mk1lMMtaWKGlJSTB6NHz1lfY8MBDWrNGmrdSTfPfLB/kciyYzE+bPh+nT4eZNsLCAMU/AW+HgeBPt7OVUYAJgpWuoogjke68POZMpRCnj7Axffgnr1mk/HzyoXT5ftUrvyISoGHbs0IYcGzdOKzAfbQK/NYAPQ28XmEFAJPAmUmAKUQgpMoUopZ57Do4ehTZt4MYNbaijgQO1n4UQ5nf2rDZJQqdOcOoUuFaHz56EX49D85NoPccXAfuBRvrGKkRZIEWmEKWYr692n+Zbb2mX6776Shs6JTJS78iEKD+uXNFm7PH3h59+gkqV4D//grM5MDQULBRaj/HTwEjkN6cQRST/VYQo5SwttQ5Av/wC3t5w7hw8+igsXCgzBQlxP27ehHffhYce0mbsycqCroHwex2YuxtcrqGdsdyFNvalp77xClHWSJEpRBnRpg0cOQI9ekBGhtY5qHdvbdYgIUTRpaXBvHlacTllinYLSouGsDMANh2EBmcBF2AecAT4l77xClFWSZEpRBlStao2O9C8edpg7hs3QosW2jibQojCpaVpVwDq1oUxY7SpXOv6wpo2EH4K2h8CKgGjgfPAq0jHHiHugxSZQpQxBoN2/9iBA1C7tjam5mOPwSefyOVzIfKTkgIff6yduRw9Whv70tsLlraBk39Cv/23fxn2Bk4C84FquoYsRLkgRaYQZVTLlnD4sDYVZUYGhIRA//7afWZCCLh6VRvn0tcXxo6Fy5ehpgcsbA3n4mHYfrDKBjoB4cAGoJ6uIQtRrkiRKUQZ5uKiXTL/4AOtg9DatRAQoA2/IkRFdeoUDB+udZR76y346y+oUwOWtYLz8RByAGyy0e613AdsB1rqG7MQ5ZEUmUKUcQYDvP66NtSRl5f2CzYgAL75Ru/IhHhwsrPhxx8hOBgaNYKlS7V7MB+pC+v94ewleDkcbBTQGW2sy11AG33jFqI8kyJTiHKiTRvt8nm7dtol8z59YPx4bVgWIcqrS5fgnXe0aVd79ICff9b+8OrZGH7xhPDz8OwJ7Uw/zwOHga3AY/rGLURFIEWmEOWIu7s2Jd748drzDz7QzuxcuaJvXEKYU1oabNgAXbuCj482jmx0NFR1gvGN4A8r+O44tI0FgwswHvgfsBporm/sQlQklfQOQAhhXpUqwezZ2iXzwYNh926tk9DGjdpsQUKURdnZ2oQEa9Zot4IkJf297nEfGJYKva+A7cnbC5uhzc7zPODw4OMVQkiRKUS51bu3dm9az57aLEFt2sCyZdoc6EKUBZmZWmH57bfaH0kJCX+v83aGF+xgcBzUj769sDLQD3gJrSOP4YGHLIS4gxSZQpRjjRpBeLg2tNHmzTBwoDZr0Pvva2c8hShtrl6Fbdu07+vWraZnLKvawTN20P8aPJ4ElkmAJdARGAD0QM5aClGKyK8ZIco5Z2et1+20ado8zR99BL//DuvWaTMICaGnlBRtYoHdu7X7iQ8fNp1UwNUGegLPpEP7VLBKRSssnwD6AL0AVz0iF0LcTZnp+DNjxgxat26Nvb09Li4u+baJjo6ma9eu2Nvb4+bmxvjx48n6R9faPXv20KJFC2xsbKhbty4rVqx4ANELoS8LC60H7oYNYG+v/TIPDJTxNMWDpZTWQeebb7Rhtx59VBvrtVMneO89iIjQ2jxsBZOBX4HYdFiWDp0rg1UfYCUQjzb80HCkwBSiFCszZzIzMjLo06cPQUFBLF++PM/67OxsunbtioeHBwcOHCA2NpaBAwdiZWXFzJkzAYiKiqJr164MHz6c1atXs2vXLl566SU8PT0JDg5+0IckxAPXuzfUq6cN9XL+vPZLft066NJF78hEeZOaCmfOwIkTcOwYHD2qnaXMb6QDb7Rx0dsDHQDPTLTfTq1uL+wEPIrMIy5EGWNQqmzNdrxixQrGjBlDYmKiyfKtW7fy9NNPc/nyZdzd3QFYsmQJEydO5MqVK1hbWzNx4kQ2b97M8ePHjdv17duXxMREtm3blu/rpaenk56ebnyenJyMt7c3SUlJODk5lcARClHyrlyBXr1g3z7tLOcHH8CYMdr4ggVJTk7G2dlZvvtl3F0/xwPAHqD67YcLWocaB8AOsIbMHLiWpHXEib0Mly9BTDRcvAj/i4E/LkH0X/m/viXwMBCINlRlG6AWt1+rFRAEtEYrKuX+SmEmkr/0UWbOZN5NWFgYTZo0MRaYAMHBwYwYMYITJ07QvHlzwsLC6NChg8l2wcHBjBkzpsD9zpo1i7feeqvE4hZCD66usHOnNt/5Z59p8zqfPAmLFoG1td7RibtZtGgRc+bMIS4ujqZNm7JgwQICAgLMsu/VH8HKbyEHyAYygHTgFpAMJAE3i7ivqkAjoAlaYdkceNgG7PyABkBjoOnthw/SG1yIcqbcFJlxcXEmBSZgfB4XF1dom+TkZFJTU7Gzs8uz38mTJzN27Fjj89wzmUKUddbW2pBG/v7a/XFffQWjRkHTpnpHJgqzfv16xo4dy5IlSwgMDGTu3LkEBwdz5swZ3Nzc7nv//7OBHUVoZwCqAe4G8LIAb2vwtYM6zlCnGtT3gWo1wVAD7Xq4N1AH8KAM9QYQQtwPXYvMSZMm8f777xfa5tSpUzRo0OABRZSXjY0NNjY2ur2+ECXJYNAuk/v5aUPFSIFZ+n300Ue8/PLLDBkyBNBuC9q8eTOff/45kyZNuu/995wEtbtot1FYWICNjfawt4fKlcHJSRuVwMXl9lSNQghRAF2LzNdff53BgwcX2qZOnTpF2peHhweHDh0yWRYfH29cl/tv7rI72zg5OeV7FlOIikI6/pQNGRkZREREMHnyZOMyCwsLOnToQFhYWL7b5HdfeWGaNNEeQghxv3QtMl1dXXF1Nc/4E0FBQcyYMYOEhATjJaMdO3bg5OREo0aNjG22bNlist2OHTsICgoySwxCCFGSrl69SnZ2dr63/Zw+fTrfbeS+ciGEXsrMnTHR0dEcOXKE6OhosrOzOXLkCEeOHOHmTe0W9E6dOtGoUSMGDBjA0aNH2b59O//9738JCQkxXu4ePnw4//vf/5gwYQKnT5/mk08+4euvv+a1117T89CEEKLETJ48maSkJOMjJiZG75CEEBVEmen4M3XqVFauXGl83rx5cwBCQ0Np164dlpaWbNq0iREjRhAUFISDgwODBg3i7bffNm5Tu3ZtNm/ezGuvvca8efOoWbMmn332mYyRKYQoE6pXr46lpWW+t/3k3hb0T3JfuRBCL2VunEy9JSUl4eLiQkxMjIy1JSqU3JEVEhMTcXZ21jucCiswMJCAgAAWLFgAQE5ODj4+PowaNapIHX8kh4mKSPKXPsrMmczS4saNGwAyjJGosG7cuCFJWkdjx45l0KBBtGzZkoCAAObOnUtKSoqxt/ndSA4TFZnkrwdLisxi8vLyIiYmhsqVK2MoYHqU3L+Y5EyBecn7WnKK8t4qpbhx4wZeXl4PODpxp+eee44rV64wdepU4uLiaNasGdu2bcvTGaggksP0I+9rybnbeyv5Sx9yubwEyPRVJUPe15Ij7624k3wfSoa8ryVH3tvSqcz0LhdCCCGEEGWHFJlCCCGEEMLsLKdPnz5d7yDKI0tLS9q1a0elSnLbqznJ+1py5L0Vd5LvQ8mQ97XkyHtb+sg9mUIIIYQQwuzkcrkQQgghhDA7KTKFEEIIIYTZSZEphBBCCCHMTopMIYQQQghhdlJkCiGEEEIIs5Mi08wWLVpErVq1sLW1JTAwkEOHDukdUpk3ffp0DAaDyaNBgwZ6h1Um7d27l27duuHl5YXBYOD77783Wa+UYurUqXh6emJnZ0eHDh04d+6cTtEKPUgOMz/JYeYh+avskSLTjNavX8/YsWOZNm0ahw8fpmnTpgQHB5OQkKB3aGWev78/sbGxxsf+/fv1DqlMSklJoWnTpixatCjf9bNnz2b+/PksWbKEgwcP4uDgQHBwMGlpaQ84UqEHyWElR3LY/ZP8VQYpYTYBAQEqJCTE+Dw7O1t5eXmpWbNm6RhV2Tdt2jTVtGlTvcModwD13XffGZ/n5OQoDw8PNWfOHOOyxMREZWNjo9auXatHiOIBkxxWMiSHmZ/kr7JBzmSaSUZGBhEREXTo0MG4zMLCgg4dOhAWFqZjZOXDuXPn8PLyok6dOvTv35/o6Gi9Qyp3oqKiiIuLM/kOOzs7ExgYKN/hCkByWMmSHFayJH+VTlJkmsnVq1fJzs7G3d3dZLm7uztxcXE6RVU+BAYGsmLFCrZt28bixYuJiori8ccf58aNG3qHVq7kfk/lO1wxSQ4rOZLDSp7kr9JJJvgUpV6XLl2MPz/88MMEBgbi6+vL119/zdChQ3WMTAgh7k5ymKio5EymmVSvXh1LS0vi4+NNlsfHx+Ph4aFTVOWTi4sL9evX5/z583qHUq7kfk/lO1wxSQ57cCSHmZ/kr9JJikwzsba25pFHHmHXrl3GZTk5OezatYugoCAdIyt/bt68yR9//IGnp6feoZQrtWvXxsPDw+Q7nJyczMGDB+U7XAFIDntwJIeZn+Sv0sly+vTp0/UOorxwcnJiypQpeHt7Y2Njw5QpUzhy5AjLly/H0dFR7/DKrHHjxmFjYwPAyZMnGT58OAkJCSxZsgQHBwedoytbbt68ycmTJ4mLi2Pp0qUEBgZiZ2dHRkYGLi4uZGdnM3PmTBo1akRGRgavvvoqt27dYsGCBVSqJHfXlHeSw0qG5DDzkPxVBundvb28WbBggfLx8VHW1tYqICBA/d///Z/eIZV5zz33nPL09FTW1taqRo0a6rnnnlPnz5/XO6wyKTQ0VAF5HoMGDVJKacOATJkyRbm7uysbGxvVvn17debMGX2DFg+U5DDzkxxmHpK/yh6DUkrpVeAKIYQQQojySe7JFEIIIYQQZidFphBCCCGEMDspMoUQQgghhNlJkSmEEEIIIcxOikwhhBBCCGF2UmQKIYQQQgizkyJTCCGEEEKYnRSZQgghhBDC7KTIFEIIIYQQZidFphBCCCGEMDspMkWpd+XKFTw8PJg5c6Zx2YEDB7C2tmbXrl06RiaEEIWT/CUqMpm7XJQJW7ZsoWfPnhw4cAA/Pz+aNWtGjx49+Oijj/QOTQghCiX5S1RUUmSKMiMkJISdO3fSsmVLfv/9d8LDw7GxsdHEnH1/AAAgAElEQVQ7LCGEuCvJX6IikiJTlBmpqak0btyYmJgYIiIiaNKkid4hCSFEkUj+EhWR3JMpyow//viDy5cvk5OTw4ULF/QORwghikzyl6iI5EymKBMyMjIICAigWbNm+Pn5MXfuXH7//Xfc3Nz0Dk0IIQol+UtUVFJkijJh/PjxfPPNNxw9ehRHR0eeeOIJnJ2d2bRpk96hCSFEoSR/iYpKLpeLUm/Pnj3MnTuXr776CicnJywsLPjqq6/Yt28fixcv1js8IYQokOQvUZHJmUwhhBBCCGF2ciZTCCGEEEKYnRSZQgghhBDC7KTIFEIIIYQQZidFphBCCCGEMDspMoUQQgghhNlJkSmEEEIIIcxOikwhhBBCCGF2UmQKIYQQQgizkyJTCCGEEEKYnRSZQgghhBDC7KTIFEIIIYQQZidFphBCCCGEMDspMoUQQgghhNlJkSmEEEIIIcxOikwhhBBCCGF2UmQKIYQQQgizkyJTCCGEEEKYnRSZQgghhBDC7KTIFHf1+++/07t3b3x9fbG1taVGjRp07NiRBQsWmLSbOXMm33//vU5Rws2bN5k2bRqdO3ematWqGAwGVqxYUWD7U6dO0blzZxwdHalatSoDBgzgypUredrl5OQwe/Zsateuja2tLQ8//DBr164twSMRQtypvOaghQsX0rBhQ2xsbKhRowZjx44lJSUlT7vz58/Tu3dvqlSpgr29PW3atCE0NLTU7VOIPJQQhfj111+VtbW1qlu3rnrnnXfUp59+qqZOnao6deqkHnroIZO2Dg4OatCgQfoEqpSKiopSgPLx8VHt2rVTgPriiy/ybRsTE6OqV6+uHnroITVv3jw1Y8YMVaVKFdW0aVOVnp5u0nbSpEkKUC+//LJatmyZ6tq1qwLU2rVrH8BRCVGxldccNGHCBAWo3r17q8WLF6vRo0erSpUqqU6dOpm0i46OVtWrV1fu7u5qxowZau7cuapp06aqUqVK6pdffik1+xQiP1JkikI99dRTytXVVV2/fj3Puvj4eJPneif4tLQ0FRsbq5RSKjw8vNAEP2LECGVnZ6cuXrxoXLZjxw4FqKVLlxqX/fnnn8rKykqFhIQYl+Xk5KjHH39c1axZU2VlZZXMwQghlFLlMwddvnxZVapUSQ0YMMBk+YIFCxSgfvzxR+OykSNHqkqVKqnTp08bl6WkpChvb2/VokWLUrNPIfIjl8tFof744w/8/f1xcXHJs87Nzc34s8FgICUlhZUrV2IwGDAYDAwePNi4/tKlS7z44ou4u7tjY2ODv78/n3/+ucn+9uzZg8FgYP369bzxxht4eHjg4OBA9+7diYmJuWusNjY2eHh4FOm4vv32W55++ml8fHyMyzp06ED9+vX5+uuvjct++OEHMjMzGTlypMmxjhgxgj///JOwsLAivZ4Q4t6UxxwUFhZGVlYWffv2NVme+3zdunXGZfv27aN58+b4+fkZl9nb29O9e3cOHz7MuXPnSsU+hchPJb0DEKWbr68vYWFhHD9+nMaNGxfY7quvvuKll14iICCAYcOGAfDQQw8BEB8fz6OPPorBYGDUqFG4urqydetWhg4dSnJyMmPGjDHZ14wZMzAYDEycOJGEhATmzp1Lhw4dOHLkCHZ2dvd9TJcuXSIhIYGWLVvmWRcQEMCWLVuMzyMjI3FwcKBhw4Z52uWub9OmzX3HJITIX3nMQenp6QB59mVvbw9ARESESdsqVark2cedbevVq6f7PoXIl96nUkXp9vPPPytLS0tlaWmpgoKC1IQJE9T27dtVRkZGnrYFXaoaOnSo8vT0VFevXjVZ3rdvX+Xs7Kxu3bqllFIqNDRUAapGjRoqOTnZ2O7rr79WgJo3b16R4y7sUlXuui+//DLPuvHjxytApaWlKaWU6tq1q6pTp06edikpKQpQkyZNKnJMQojiK485KCIiQgHqnXfeMVm+bds2BShHR0fjsm7duikXFxeTeJRSKigoSAHqgw8+KBX7FCI/crlcFKpjx46EhYXRvXt3jh49yuzZswkODqZGjRr8+OOPd91eKcW3335Lt27dUEpx9epV4yM4OJikpCQOHz5sss3AgQOpXLmy8Xnv3r3x9PQ0OcN4P1JTUwHt0tY/2dramrRJTU0tUjshRMkojzmoRYsWBAYG8v777/PFF19w4cIFtm7dyiuvvIKVlZVJXhkxYgSJiYk899xzREZGcvbsWcaMGcNvv/0G/J2D9N6nEPmRIlPcVatWrdi4cSPXr1/n0KFDTJ48mRs3btC7d29OnjxZ6LZXrlwhMTGRZcuW4erqavIYMmQIAAkJCSbb1KtXz+S5wWCgbt26XLhwwSzHk3vpJ/dS0J3S0tJM2tjZ2RWpnRCi5JS3HATafeFNmzblxRdfpHbt2nTr1o1nn32W5s2b4+joaGzXpUsXFixYwN69e2nRogV+fn5s3ryZGTNmAJi01XOfQuRH7skURWZtbU2rVq1o1aoV9evXZ8iQIWzYsIFp06YVuE1OTg4AL7zwAoMGDcq3zcMPP1wi8RbE09MTgNjY2DzrYmNjqVq1qvHspaenJ6GhoSilMBgMJu0AvLy8HkDEQggoPzkIoEaNGuzfv59z584RFxdHvXr18PDwwMvLi/r165u0HTVqFEOGDOHYsWNYW1vTrFkzli9fDmDSVu99CvFPUmSKe5LbaebOQu3OIiyXq6srlStXJjs7mw4dOhRp37k9G3MppTh//rzZfhHUqFEDV1dX46WhOx06dIhmzZoZnzdr1ozPPvuMU6dO0ahRI+PygwcPGtcLIR68spyD7lSvXj3jmdOTJ08SGxtr0is+l4ODA0FBQcbnO3fuxM7Ojscee6xU7VOIO8nlclGo3LN4/5R7b9KdQ2A4ODiQmJho0s7S0pJevXrx7bffcvz48Tz7yW+GnS+//JIbN24Yn3/zzTfExsbSpUuXez6Of+rVqxebNm0yGZZk165dnD17lj59+hiX9ejRAysrKz755BPjMqUUS5YsoUaNGrRu3dpsMQkh8iqvOeifcnJymDBhAvb29gwfPrzQtgcOHGDjxo0MHToUZ2fnUrtPIQwqv/+9QtzWuHFjbt26xb///W8aNGhARkYGBw4cYP369Xh7exMZGWkcv65r16788ssvvP3223h5eVG7dm0CAwOJj48nMDCQK1eu8PLLL9OoUSOuXbvG4cOH2blzJ9euXQO0MeqefPJJmjRpgsFgYMiQIcTHxzN37lxq1qzJ0aNHjUNnFGThwoUkJiZy+fJlFi9ezDPPPEPz5s0BGD16tDF5xsTE0Lx5c1xcXPjPf/7DzZs3mTNnDjVr1iQ8PNyks8+ECROYM2cOw4YNo1WrVnz//fds3ryZ1atX8/zzz5fE2y6EuK285qD//Oc/pKWl0axZMzIzM1mzZg2HDh1i5cqVDBgwwLi/ixcv8uyzz9K9e3c8PDw4ceIES5YsoUGDBvzyyy8mHZT03KcQ+dKnU7soK7Zu3apefPFF1aBBA+Xo6Gic3m306NF5Zts4ffq0atu2rbKzs1OAyVAi8fHxKiQkRHl7eysrKyvl4eGh2rdvr5YtW2Zskzt8yNq1a9XkyZOVm5ubsrOzU127djWZmacwvr6+Csj3ERUVZdL2+PHjqlOnTsre3l65uLio/v37q7i4uDz7zM7OVjNnzlS+vr7K2tpa+fv7q1WrVhX9TRRC3LPymoO++OIL1bRpU+Xg4KAqV66s2rdvr3bv3p1nf9euXVM9evRQHh4eytraWtWuXVtNnDgxz/BDeu9TiPzImUxRauSeRdiwYQO9e/fWOxwhRAUjOUgI85J7MoUQQgghhNlJkSmEEEIIIcxOikwhhBBCCGF2ck+mEEIIIYQwOzmTKYQQQgghzE6KTCGEEEIIYXYyrWQx5eTkcPnyZSpXrpzvFGZClFdKKW7cuIGXlxcWFvL3aVklOUxURJK/9CFFZjFdvnwZb29vvcMQQjcxMTHUrFlT7zDEPZIcJioyyV8PlhSZxZQ73VZMTAxOTk46RyPEg5OcnIy3t7fJlHOi7JEcJioiyV/6kCKzmHIvLzk5OUmCFhWSXGIt2ySHiYpM8teDJTcmCCGEEEIIs5MiUwghhBBCmJ0UmUII+Ao4qncQQghRfJk3YX43SE3QOxLxT3JPZgnJzs4mMzNT7zCEuLs/gXeBTOAboFH+zTIyMvD19SUjI4O0tLQHF185YmVlhaWlpd5hFInkMFFWrBgFH/0OO5+A9RFgyOf0meQv8yhuDpNpJYspOTkZZ2dnkpKS8r1pXilFXFwciYmJOkQnxD1IAFIBW8C94GY5OTnExMTg7e0t48zdBxcXFzw8PHTrgCA5TJQn2elwKQ4UUNURKlfLv53kL/MpTg6TM5lmlpuc3dzcsLe3l55sonRLBlIgwwGs6oLBtuCm2dnZpKamUqtWrTJzNq40UUpx69YtEhK0a3qenp46R5Q/yWGiLIk5A9Wqg50B6jSCgr6ukr/u373kMCkyzSg7O9uYnKtVK+DPKSFKixwgXvvnfCWwjIU6dcDGJv/m2dnZANja2kqSvkd2dnYAJCQk4ObmVureR8lhoiy5EQdJt+/oqFULbv/3ypfkL/Mobg6Tc8ZmlHv/kr29vc6RCFEEcUA6xFpAWhZkZIDk3pKXmx9K4/2OksNEWZGTDdGXtJ9d7cBB/iZ6YIqTw6TILAFyeUmUemlALNwC4nK0RT4+UEmubZS4spAfykKMomJL+ANSlXY5tkZdvaOpWIqTH6TIFKKiUUA0KAUXLLWnLi5QpYregQkhxN1l3ITLydrPNV2hUgG3+Aj9SZEpREVzHUiGeOBWtnaJ3MdH76CK7/XXX8dgMPDMM88Y77cSQpRzCqL/0O4ld7SEamUwd0HFyV9SZAqzy8zMZOLEiTRp0gQHBwe8vLwYOHAgly9fvuu2ixYtolatWtja2hIYGMihQ4dM1qelpRESEkK1atVwdHSkV69exMfHl9ShGF9z8ODBNGnShEqVKtGzZ88ibXft2jX69++Pk5MTLi4uDB06lJs3b5q0OXbsGI8//ji2trZ4e3sze/bskjiEv2UDMdrV8ku3r3h4e4O19d9Nli1bRrt27XBycsJgMBR5KJsH+dnNnDmTZcuWsXTpUsLCwhg+fHieNnv27KFHjx54enri4OBAs2bNWL169T29nqg4JH9pSmX+ApIuQ+LtWwF9auftTS75q3SRIlOY3a1btzh8+DBTpkzh8OHDbNy4kTNnztC9e/dCt1u/fj1jx45l2rRpHD58mKZNmxIcHGwcLgHgtdde46effmLDhg388ssvXL58mWeeeabAfe7Zs4datWrd1/FkZ2djZ2fHq6++SocOHYq8Xf/+/Tlx4gQ7duxg06ZN7N27l2HDhhnXJycn06lTJ3x9fYmIiGDOnDlMnz6dZcuW3Ve8/2QwGLhw4YL25BKoTLhg0C6XOznBPzsR37p1i86dO/PGG28U+TVK4rMryLJly/jggw/YuXMnw4YNY+/evWzfvp3JkyebtDtw4AAPP/ww3377LceOHWPIkCEMHDiQTZs2Ffs1RcUh+UtTGvNXdiZcjNWWuzuAvUve9pK/ShkliiUpKUkBKikpKc+61NRUdfLkSZWamvr3whyl1E2dHjlFO6aVK1eqqlWrqrS0NJPlPXr0UC+88ELRdnIXhw4dUoC6ePFigW0CAgJUSEiI8Xl2drby8vJSs2bNUkoplZiYqKysrNSGDRuMbU6dOqUAFRYWlu8+Q0NDla+vr1mOQSmlBg0apHr06HHXdidPnlSACg8PNy7bunWrMhgM6tKlS0oppT755BNVpUoVlZ6ebmwzceJE5efnp5TSvk+NGjVSL7/8snH9+fPnlaOjo1q+fHmRYwZUVFSU9p0IVyo+XKnwcKUiIpT6x0duIjQ0VAHq+vXrSimlsrKyVHh4uMrKysrT1hyf3VtvvaU8PT3V1atXjW2eeuop1a5dO5Wdna2UUmrDhg3Kw8NDHTlyxOT1L168qOrWras+/PDDQt+Lp556Sg0ZMqTQNiUt3zzxABUrh0n+UkpJ/lKqFOQvpVTMSS13HQ1XKiuj8O0kf5Wc4uQwOZNZ0m4Bjjo9bhUtxD59+pCdnc2PP/5oXJaQkMDmzZt58cUXAdi3bx+Ojo6FPgo7lZ+UlITBYMDFJZ8/PdGm/IqIiDD5S9vCwoIOHToQFhYGQEREBJmZmSZtGjRogI+Pj7FNaREWFoaLiwstW7Y0LuvQoQMWFhYcPHjQ2KZt27ZY33GtOjg4mDNnznD9+nVsbW1ZvXo1K1eu5IcffiA7O5sXXniBjh07Gj+XIlPARUgH/rx9ealmzYLHxCwOc312b775JrVq1eKll14CtMtXBw4cYOXKlcYZOnr37k1sbCxNmzY1icHHx4dz584xduzYQmNNSkqiatWq93/QFYXkL0DyF+icv4DU6xCfov3s4wmWVvd3jLkkf5UsGbBEYGdnx/PPP88XX3xBnz59AFi1ahU+Pj60a9cOgJYtW3LkyJFC9+Punv+chGlpaUycOJF+/frlO40dwNWrV8nOzs6zD3d3d06fPg1oM5FYW1vnSfTu7u7ExcXd9TgfpLi4ONzc3EyWVapUiapVqxpjjYuLo3bt2iZtco8/Li6OKlWq0KxZM959911eeukl+vbty8WLF+/tcslVUAa4AOQocHQEV9d7ObJ8dm2mz87S0pJVq1bRrFkzJk2axPz58/nss8/wMVOvpK+//prw8HCWLl1qlv2J0kHyl/mVtvylcuBi1O2RMKzApca9HVd+JH+VLCkyS5o9cPOurUrutYvo5ZdfplWrVly6dIkaNWqwYsUKBg8ebBwPy87Ojrp1iz8YWWZmJs8++yxKKRYvXlzs7e+Fo6Oj8efs7GzS09NNlr3wwgssWbIk3239/f25ePEiAI8//jhbt24t2WCL4PXXX+f7779n4cKFbN269a4zsXTp0oV9+/aZLPNv6w8GAwrw9PTlxIkTBU6/pqc6derwwQcf8Morr/Dcc8/x/PPPm2W/oaGhDBkyhE8//RR/f3+z7LNCkPwl+es+mSN/NW7sj0L7LGv5+nLy1IkSi/d+SP7KS4rMkmYAHPQO4u6aN29O06ZN+fLLL+nUqRMnTpxg8+bNxvX79u2jS5cuhe5j6dKl9O/f3/g8N0FfvHiR3bt3F3gWAKB69epYWlrm6a0XHx+Ph4cHAB4eHmRkZJCYmGjyF+WdbQCTMxYHDx5k4sSJ7Nmzx7issDi2bNlinMXArrA5yu7Cw8PD5KZxgKysLK5du2ZyPPkdb+66XAkJCZw9exZLS0vOnTtH586dC33tzz77jNTUVOPzevXq8f3cLdxyq0EO4O1thW0hc5QXlzk/O4C9e/diaWnJhQsXyMrKotJ9jhD/yy+/0K1bNz7++GMGDhx4X/uqcCR/Sf66Tc/8Ne/jLVRzq4GnE3jWNdN18tskf5WwEr9DtJwpdsefMuSTTz5R9evXVyEhIapTp04m627duqXOnTtX6CM5OdnYPiMjQ/Xs2VP5+/urhISEIr1+QECAGjVqlPF5dna2qlGjRp6br7/55htjm9OnT5fqG+d/++0347Lt27fne+N8Rsbfd7BPnjzZeON8ri5duqgnn3xSrVq1StnZ2amTJ08WPeBr2o3zO3+IUuHhSp06pVROETtUFPfGeXN8duvWrVN2dnZq3759ytPTU02dOrXox1rAMTg4OKiFCxfe137MSe88UV5zmOSvuytz+Utp+euHH6LUiQilcrKLvp3kr5JTnDxRrorMrKws9d///lfVqlVL2draqjp16qi3335b5dzxWzUnJ0dNmTJFeXh4KFtbW9W+fXt19uzZIr9GeU3QSmn/kezt7ZW1tbVat27dPe8nIyNDde/eXdWsWVMdOXJExcbGGh939kT817/+pRYsWGB8vm7dOmVjY6NWrFihTp48qYYNG6ZcXFxUXFycsc3w4cOVj4+P2r17t/rtt99UUFCQCgoKKjAWcyXpEydOqMjISNWtWzfVrl07FRkZqSIjI43rDx48qPz8/NSff/5pXNa5c2fVvHlzdfDgQbV//35Vr1491a9fP+P6xMRE5e7urgYMGKCOHz+u1q1bp+zt7dXSpUuNbRYuXKhcXFxUdHS0Ukqpfv36qebNm5u8jwXKVEod+TtJR0QoVZSvZmxsrIqMjFSffvqpAtTevXtVZGSkSkhIMCbpkvjsYmJiVJUqVdT8+fOVUkpt27ZNVapUqcBfwHeze/duZW9vryZPnmzyHfzrr7/uaX/mUliekBx27yR/FaxM5i+l1PU//85fKUX8byv5q+RV2CJzxowZqlq1amrTpk0qKipKbdiwQTk6Oqp58+YZ27z33nvK2dlZff/99+ro0aOqe/fuqnbt2kVOquU1QecaMGBAvsOBFEdUVJRCu0c7zyM0NNTYztfXV02bNs1k2wULFigfHx9lbW2tAgIC1P/93/+ZrE9NTVUjR45UVapUUfb29urf//63io2NLTAWcyVpX1/ffI/nztfhjqE2lFLqr7/+Uv369VOOjo7KyclJDRkyRN24ccNkv0ePHlVt2rRRNjY2qkaNGuq9994zrjt16pSys7NTa9asMS67fv268vb2VhMmTLh70BeUSg3/O0nHxxftWKdNm5bvsS5fvtyYpM392eXk5Kj27dur4OBgk4Jq9OjR6qGHHsrzvhXFoEGD8j2OJ554otj7MqfC8oTksPsj+St/ZTF/ZaVrQxUB6tcdUXdtn0vyV8krTp4wKKXU/V5yLy2efvpp3N3dWb58uXFZr169sLOzY9WqVSil8PLy4vXXX2fcuHGANiSAu7s7K1asoG/fvnn2mZ6eTnp6uvF5cnIy3t7eJCUl5bk3Ji0tjaioKGrXro2tOW96e4Dat2+Pv78/8+fP1zsUcT9ugDoDZ9D6bVSuDPXr550doziys7OJjIykefPmWFpamivSCqewPCE57P5I/io/ok9AQirYGKDRw/c/ZJHkL/MpTp4oV+Nktm7dml27dnH27FkAjh49yv79+403fEdFRREXF2cy1pWzszOBgYEFjlM2a9YsnJ2djQ9vb++SPxAdXL9+ne+++449e/YQEhKidzjifuQAF7W5yW8CFhZQq9b9FZjiwZAcdm8kf5UvN69oBSaAbw3zjYkpHrxy1bt80qRJJCcn06BBAywtLcnOzmbGjBnGHoO541nlNx5WQeOUTZ482WSA1NyzAOVN8+bNuX79Ou+//z5+fn56hyPuRyzcSoNLt596e5tn0HVR8iSH3RvJX+VHThZciNZ+rmYDTh6FtxelW7kqMr/++mtWr17NmjVr8Pf358iRI4wZMwYvLy8GDRp0T/u0sbHBpgL8hjbObS3KtluQEwtRaDfwODtD9ep6ByWKSnLYvZH8VX7EnYc0pRUn3vX0jkbcr3JVZI4fP55JkyYZ70tq0qQJFy9eZNasWQwaNMg4nlV8fDyenp7G7eLj42nWrJkuMQthNgq4ALFAKlCpklwmL2skh4mKLPU6xN4e/N/HHSqVvduCxT+Uq3syb926ZZwjNJelpSU5OTkA1K5dGw8PD3bt2mVcn5yczMGDBwkKCnqgsQphdnFw85ZWZAL4+oKV3MtUpkgOExWVyoELd0wdWaWm3hEJcyhXZzK7devGjBkz8PHxwd/fn8jISD766CNefPFFAAwGA2PGjOHdd9+lXr161K5dmylTpuDl5UXPnj11jl6I+5AK2Ze1y+QA1apBlSq6RiTugeQwUVHFn4eUHLAEfOrJFZjyolwVmQsWLGDKlCmMHDmShIQEvLy8eOWVV5g6daqxzYQJE0hJSWHYsGEkJibSpk0btm3bViaH6xACMF4mj1GQDlhba519RNkjOUxURGmJcClZ+9m7OlgXY956UbqVq3EyH4Tk5GScnZ3L5RhzooyKg+t/wh+3n/r5aeNimpuMM2ceeucJyWGiNFE5cOYI3MwBp0pQr2nJnMWU/GU+FXacTCEqnDTIuAQXbz/18CiZAlMIIUpCwh9agWkB+NaVy+TljRSZokwZPHiw3HuWS4GKggsKsgB7e/Dy0juo8iMnJ4c+ffpgMBj4z3/+o3c4opyQHPa3tCT4M0n72bsa2DjqG095tGDBAgwGA61bt+bWrVsP/PWlyBQVyowZM2jdujX29va4uLgUaZvBgwdjMBhMHp07d77v/d6LRYsWUatWLWxtbQl8JJBthw6RDFgYoHZtbXaff9qwYQMNGjTA1taWJk2asGXLFuO6zMxMJk6cSJMmTXBwcMDLy4uBAwdy+fLlEjsGgOjoaLp27Yq9vT1ubm6MHz+erKysQrc5e/YsPXr0oHr16jg5OdGmTRtCQ0NN2oSHh9O+fXtcXFyoUqUKwcHBHD169J5iHDFiBPv372fp0qV8/vnnvPvuu3nabNy4kY4dO+Lq6oqTkxNBQUFs3779nl5PiKK4l1xz8+ZNRo0aRc2aNbGzs6NRo0YsWbLEpM0ff/zBv//9b+N3+dlnnyU+Pt7s8d+Zjx5+pAn7f92CUyWoXqvgbRYtWkTDhg2xs7PDz8+PL7/8Mk+bxMREQkJC8PT0xMbGhvr165vkOnPbuHEjnTp1olq1ahgMBo4cOVKk7QrLxwBKKaZOnYqnpyd2dnZ06NCBc+fO3VOMq1evZty4ccyfP59r167Rq1cvMjMzTdocPXqUfv364e3tjZ2dHQ0bNmTevHn39Hr5kSJTPHAZGRm6vnafPn0YMWJEsbbr3LkzsbGxxsfatWvva7979uyhVq1axYph/fr1jB07lmnTpnH4wGH8azXludHBXLuWQE1vsLPLu82BAwfo168fQ4cOJTIykp49e9KzZ0+OHz8OaEPmHD58mClTpnD48GE2btzImTNn6N69e7Fi+6datWqxZ8+efNdlZ2fTtWtXMjIyOHDgACtXrmTFihUmnVvy8/TTT5OVlcXu3buJiIigadOmPP3008aZbjrhcecAACAASURBVG7evEnnzp3x8fHh4MGD7N+/n8qVKxMcHJwnsd7NG2+8wbZt29i7dy/Dhg1jx44dfPTRRyxdutSk3d69e+nYsSNbtmwhIiKCJ598km7duhEZGVms1xNlS1nLYWPHjmXbtm2sWrWKU6dOMWbMGEaNGsWPP/4IQEpKCp06dcJgMLB7925+/fVXMjIy6Natm3H4rH+6cOEChmJe274zH/38XSSPP9GTceN6kpJxvMDL5IsXL2by5MlMnz6dEydO8NZbbxESEsJPP/1kbJORkUHHjh25cOEC33zzDWfOnOHTTz+lRo0axYrvTtOnT2fw4MEFrk9JSaFNmza8//77Rd7n3fIxwOzZs5k/fz5Llizh4MGDODg4EBwcTFpaWrHi37JlC8OHD2fDhg2MHj2avXv3cvnyZQYPHsydXXEiIiJwc3Nj1apVnDhxgjfffJPJkyezcOHCYr1egZQolqSkJAWopKSkPOtSU1PVyZMnVWpqqnFZTo5SN2/q88jJKdoxrVy5UlWtWlWlpaWZLO/Ro4d64YUXCt122rRpqmnTpmrJkiWqZs2ays7OTvXp00clJiYa2wwaNEj16NFDvfvuu8rT01PVqlVLKaVUdHS06tOnj3J2dlZVqlRR3bt3V1FRUcbtsrKy1GuvvaacnZ1V1apV1fjx49XAgQNVjx49inZghfjiiy+Us7Nzkdrmxm/O/YaGhipfX98i7TNXQECACgkJUSpHqawTSh09mK1cXb3UuHGzCvysn332WdW1a1eTZYGBgeqVV14p8HUOHTqkAHXx4kWllPb9cHBwUKdOnVLh4eEqKytLjRgxQvn5+amUlJR89+Hr66tCQ0PzXbdlyxZlYWGh4uLijMsWL16snJycVHp6er7bXLlyRQFq7969xmXJyckKUDt27FBKKRUeHq4AFR0dbWxz7NgxBahz584ppZQaMmSIatKkifG7np6erpo1a6YGDBhg3Oajjz5SdevWNR5/rsjISOXh4aE2bNiQb4y5GjVqpN56660C1+eXJx6k4uSwspC/lJIcdjf+/v7q7bffNlnWokUL9eabbyqllNq+fbuysLAw+U4kJiYqg8Fg/P/1T1FRUaq4JURuPrp1TanfwpUKD1fqkWaF56OgoCA1btw4k2Vjx45Vjz32mPH54sWLVZ06dVRGRka++0hISFDu7u5q5MiRKisrSyml1K+//qqsrKzUzp07891m2rRpatCgQXc9ptz3ITIy8q5t75aPc3JylIeHh5ozZ45xfWJiorKxsVFr165VSv2dj8+ePWts8898vH//flW9enX1888/m7zWtWvXVEBAgBo9enShcY4cOVI9+eSTBa4vTg6TM5kl7NYtcHTU51HU2y/69OlDdna28a9agISEBDZv3mwcn68w58+f5+uvv+ann35i27ZtREZGMnLkSJM2u3bt4syZM+zYsYNNmzaRmZlJcHAwlStXZt++ffz66684OjrSuXNn41mCDz/8kBUrVvD555+zf/9+rl27xnfffWey35kzZ+Lo6FjoIzo6umhvRCH27NmDm5sbfn5+jBgxgr/++uu+91kcGRkZRERE0KFDB4iDmFuQYWFBYGAHTp8OK/AsQFhYmLbNHYKDgwkLCyvwtZKSkjAYDMZLcQMHDuSpp55iwIABZGVlsXnzZj777DNWr16NvX3xxxoJCwujSZMmJvNvBwcHk5yczIkTJ/Ldplq1asbLZCkpKWRlZbF06VLc3Nx45JFHAPDz86NatWosX76cjIwMUlNTWb58OQ0bNjSeNZ4/fz4pKSlMmjQJgDfffJPExESTv9pfe+01zp07h4+Pj0kMzZo1IzY2lt69exd4bDk5Ody4cYOqVasW+30pjcpC/gLJYXfTunVrfvzxRy5duoRSitDQUM6ePUunTp0ASE9Px2AwmEw/amtri4WFBfv377+v175TWFgY7f/Vgajbg647V4KnuhWej9LT0/P0YLazs+PQoUPGKxQ//vgjQUFBhISE4O7uTuPGjZk5cybZ2dkAuLq68umnn7Js2TJ+++03bty4wYABAxg1ahTt27c32/Hdzd3ycVRUFHFxcSZtnJ2dCQwMNLbJzcf9+/cvMB8/9thjXLlyhY4dO5q8VpUqVTh48CDz588vNM6kpCTz5bC7lqHCRHHPZN68qRTo87h5s+jHNWLECNWlSxfj8w8//FDVqVNH5dzldMK0adOUpaWl+vPPP43Ltm7dqiwsLFRsbKxSSjsL4O7ubnKW6quvvlJ+fn4m+09PT1d2dnZq+/btSimlPD091ezZs43rMzMzVc2aNU3OAvz111/q3LlzhT4yMzPzxF2cswBr165VP/zwgzp27Jj67rvvVMOGDVWrVq2MfxHfy36Leybz0qVLClAHdh9Qf90+AxAertSrr45XAQEBBW5nZWWl1qxZY7Js0aJFys3NLd/2qampqkWLFur55583WX7t2jVVs2ZN1atXL+Xu7q5mzJhRaLyFncl8+eWXVadOnUyWpaSkKEBt2bKlwH3GxMSoRx55RBkMBmVpaak8PT3V4cOHTdr8/vvv6qGHHlIWFhbKwsJC+fn5qQsXLpi0OXDggLKyslJTpkxRlSpVUvv27Sv0WIrj/fffV1WqVFHx8fEFtilLZzLLSv5SSnJYYdLS0tTAgQPV/7d353E21v//xx+zHoNZjGXGCFH2NYShUsyHRLTSolSiLEXSD30S9SkqbR99spXt45Ml9ZVQSpOQPVuKJjthZiIzw2C28/79cZmTw2BwxjXnzPN+u52bc13nOpfXOXOd13md63ovgAkMDDTBwcFm2rRprseTk5NNWFiY6d+/v0lPTzfHjx83/fr1M4Dp1atXnvu8nDOZQUFB5sO3Z5h164zZsM6YjPQL5yNjjBk6dKiJjo42P/30k3E6nWbdunUmKirKAObgwYPGGGNq1KhhHA6HeeKJJ8xPP/1kZs2aZSIjI82IESNc+8nOzjb33XefqV69unnooYfcrmjkpSDOZF4sH69YscLtdeW6//77TZcuXVzLufm4d+/e+crHl2LFihUmMDDQdQzn5VJymE8Nxl4YFS8Ox4/b93/nV8+ePbnxxhs5cOAAFSpUYOrUqa4OLxdTqVIlt7YvsbGxOJ1OEhISXHMt16tXj+DgYNc2mzdvZseOHYSeNd7OqVOn2LlzJ6mpqRw6dIhmzZq5HgsMDKRJkyZu7UkiIyML/KxR7jzSYL2O+vXrc9111/HDDz9c0q/gkiX/7jqZk5NDRkaG27pu3boxfvx4li9fTvv27V3rJ0yYwG233QacHq6oprW+fDScceLhimVlZdGlSxeMMYwbN87tsVKlSjFx4kTuuOMOYmNjXWcCcz399NP873//cy2fOHGC9u3bu41Hd/wKPgjGGPr27Uu5cuVYvnw5ISEhfPzxx9x5552sW7eO8uXLc/LkSXr06EHLli2ZOXMmOTk5vP3223To0IF169YRcrrRamxsLIMGDeJf//oXgwcP5qabbrrsuM40Y8YMXnnlFebNm0e5cuU8sk+7eUv+AuWwC/nggw9YvXo1X375JZUrV2bZsmX07duXmJgY4uLiKFu2LHPmzKF3796MGTMGf39/HnzwQRo1auQ2zWmdOnXYu9caMC33NZyZw26++Wa+/vpr9u3bR+3atV3rX3zxRV588UUAjp5uWlipXP4GXR82bBiJiYk0b94cYwxRUVF0796dt956yxWb0+mkXLlyTJw4kYCAABo3bsyBAwcYPXo0w4cPd+2rf//+dO/enTlz5rB+/Xq3M7dn593MzEyMMXz22WeudRMmTODhhx++eNAFrFSpUkyaNIl27drRokWLc/Lx5frll1/o3Lkzw4cPd53lvlIqMguYnx+UKGF3FBd3ww030KBBA/773//Stm1bfv31VxYuXOix/Zc46004fvw4jRs35pNPPjln27Jly+Z7vyNHjmTkyJEX3Gbr1q3nXPq8ElWrVqVMmTLs2LHjkorMM3sfrlmzhsGDB7t1jskdGLtJkyZu20ZFReFwOAgICODnxCRia0KJ4lA+BpKSklxfgnmJjo4+p4doXs/JLTD37t3L999/f84g3WAl4YCAABITE0lPT3f7cn311VcZNGiQa/nWW2/lzTffdPuCPTOmtWvXnhNT7mN5+f7771mwYAFHjx51xTZ27FgWL17MtGnTGDJkCDNmzGDPnj2sWrXK9eUzY8YMSpUqxbx581w/FpxOJytWrCAgIIAdO3bk/cZdolmzZvHkk08yZ86ccy6HeTNvyV+gHHY+J0+e5MUXX2Tu3Ll06NABgPr167Np0ybefvtt1/Hatm1bdu7cyeHDhwkMDCQiIoLo6GiqVq3q2tdXX33lukR94MABbr31VrdclftDLiYmxm19ZGQkzmwoHRnNkSNJlAqGyNOzkl0sh4WEhDB58mQmTJhAUlIS5cuXZ+LEiYSGhrre5/LlyxMUFOT2o7ZWrVokJiaSmZnp+nHwxx9/cPDgQZxOJ3v27KFevXqu7c/Ou2PGjOHAgQNuHXvObOJzOS6Wj3P/zX2dZ27TsGFDt+ctW7aMgIAADh06dE4+vhxbt26lTZs29OrVi5deeumK9nUmFZni8uSTT/L+++9z4MAB4uLiqJjPuQn37dvHwYMHiTk9SOPq1avx9/enRo0a531Oo0aNmD17NuXKlcuzoAErcaxZs4ZbbrkFgOzsbNavX0+jRo1c2zz99NN06dLlgvHFeHjwyD/++IMjR464JYH8uP766932ERgY6LYuV0hIyLnrj0G9mo35cV08N7W+i6rXATiJj4+nX79+5/0/Y2NjiY+PZ8CAAa51ixcvJjY21rWcW2Bu376dJUuWULp06XP2s3LlSkaPHs0777zDpEmT6NevH9OmTXM9Xq5cObezd4GBgVSoUCHP1xcbG8vrr79OcnKy6zmLFy8mLCzM7ezHmXLHd/M/a4wmf39/V+/XEydO4O/v73bmKnf5zB6yo0eP5rfffmPp0qW0a9eOKVOm8Pjjj+f5/+bHzJkzeeKJJ5g1a5brS1zsoRx2rqysLLKyss757AQEBOTZc7xMmTKA9cMuOTnZbaSJypUru+4HBlrlQ16f8bxy275foW69WNavi6fyyAGuduRn56PzCQoK4pprrgGsH3UdO3Z0vaaWLVsyY8YMnE6na93vv/9O+fLlXQVmZmYmL7/8Ml26dKFmzZo8+eSTbNmyxZWDzs67kZGRpKWl5fn6LtfF8nGVKlWIjo4mPj7eVVSmpaWxZs0at9EEVq5cyZtvvsn8+fMZPHjwOfn4Uv3666+0bt2a7t278/rrr1/2fvLkkYv4Rciltsn0JikpKaZ48eImODjYzJo1K1/PGT58uClRooSJi4szmzZtMsuWLTPVq1c3DzzwgGubvHpnp6enm2rVqplbb73VLFu2zOzatcssWbLEPPPMM2b//v3GGGPeeOMNExkZaebOnWu2bdtmevbsaUJDQ6+oZ+bevXvNxo0bzSuvvGJKlixpNm7caDZu3GiOHTvm2qZGjRrm//7v/4wxxhw7dswMGjTIrFq1yuzevdt89913plGjRqZatWpu7Xnys98zXVKbzCxjUjYa8/rrs0xwsMP85z9TzdatW02vXr1MRESEWy/tRx55xAwZMsS1nNu+5u233zbbtm0zw4cPN0FBQWbLli3GGGMyMzNNp06dzDXXXGM2bdpkDh065Lrltj9LS0szVatWNQMGDDDr1q0zGzduNA6H44K9rC/UJjM7O9vUrVvXtG3b1mzatMksWrTIlC1b1gwdOtS1zZo1a0yNGjVc7eT+/PNPU7p0aXPPPfeYTZs2mYSEBDNo0CATFBRkNm3aZIwxZtu2bcbhcJjevXubrVu3ml9++cV069bNhIeHu9o4bdiwwQQHB5svv/zSGGPMhAkTTGhoqNm5c2f+/hZn+eSTT0xgYKD58MMP3d67M3smn83uPKEc5s7Xc5gxxrRq1crUqVPHLFmyxOzatctMmTLFFCtWzIwdO9a1zeTJk82qVavMjh07zPTp001kZKQZOHDgeeO4lDaZqQetNuQff3zhfGSMMUOGDHEb7SEhIcFMnz7d/P7772bNmjWma9euJjIy0q0X/759+0xoaKjp16+fSUhIMAsWLDDlypUzr732mmubgQMHmpiYGPPXX3+ZnJwcc9NNN53T0/tMF2uTeeTIEbNx40azcOFCA5hZs2aZjRs3utrxGnPp+dgY65iJiIhw9QPo3LmzqVKliuszmZuPc/82P//880Xz8YVs2bLFlC1b1nTr1s0thyUnJ5/3OZeSJ1RkXiJfTtDGWB+KvIYCOZ/c4T/Gjh1rYmJiTLFixcx9991n/vrrL9c25xsC6NChQ+bRRx81ZcqUMQ6Hw1StWtX07NnT9d5mZWWZ/v37m7CwMBMREWEGDhx4xcN/dO/e3WB1bHS7nVkQAWbKlCnGGGNOnDhh2rZta8qWLWuCgoJM5cqVTc+ePd0Ku/zu90yXUmRmbDdm4+mOPq+M+MBUqlTJBAcHm6ZNm5rVq1e7bduqVatzEuOnn35qqlevboKDg02dOnXMwoULXY/lflFcKPbcYX/S09NdQxi98847JjIy0q2zxJkuVGQaY8yePXtM+/btTUhIiClTpox5/vnn3To3LFmyxABuXyTr1q0zbdu2NZGRkSY0NNQ0b978nI5C3377rWnZsqVrSJnWrVubVatWGWOsz2ft2rXP6cjQqVMn06JFizw7cl1Mq1at8nzvLvTlZHeeUA5z5+s5LDfOxx57zPX6atSoYd555x23TkuDBw82UVFRJigoyFSrVu2cx8+W3yIz66Qxm07nrz2/XDgf5b6+Vq1auZa3bt1qGjZsaEJCQkxYWJjp3Lmz+e233875f1auXGmaNWvm+ju8/vrrrs/0kiVLTGBgoPnoo49c63bv3m3CwsLcCu0zXazInDJlSp5/h+HDh7u2udR8bIw1jNGwYcNMVFSUcTgcpk2bNiYhIcH1+NnDsBljLpqPL2T48OF5vo4LfT9dSp7wM+aMFshyUWlpaYSHh5OamnrOJZJLmTS+sGrTpg116tS56BAHuUaMGMEXX3yR79kO5NKYI/D7bjgGhDigVp28Z/W5GnJycti4cSM33HCDW9snuTR25wnlMHfKYQXHGNj1MxzNgmJ+UKs+BATZE4vyl+dcSp5Qm0wB4OjRo/zwww/88MMPjB071u5wBCATDu6xCkx/P7iumn0FpkhhpxxW+BzZaxWYfkCVa+0rMMU+KjIFsHpmHj16lDfffNOtsfuZQ1ac7ewp9sSDDKRuh0OnrzNUvha89MSSyFWhHFa4nEqDfYet+zFhUOLc/oRSBKjIFMCahzYvZw5ZcbaoqChCQ0MZMWJEwQVWRGUegN0nrftlIyGPDt8icgblsMLDmQO7d4ATCA2AaM910BYvoyJTLujMISvk6nAeg12JkA0UD4aK19odkYj3Ug67+g5th3QnBABVqoGfmvkUWfrTFwD1pZLLlg0HdsBxIMAPrquudpi+xhvygzfEKIXTsSQ4dHqWqMpREFzywtuL97mU/KCvLw8KCrJaNecOHC1ySQz8tQOScqzFKteCQ+0wfU5ufsjNF4WJcphciexTsGu/db9Msb9n9RHfcik5zOculx84cIDBgwfz9ddfc+LECa6//nqmTJlCkyZNAKsCHz58OB999BEpKSm0bNmScePGUa1atSv+vwMCAoiIiCA5ORmA4sWL52veXBGAU8mw+/QZgDLhUKwEnDplb0xnysmxqt9Tp05pCJDLYIzhxIkTJCcnExERcd73UDlMvJExsDcBsoBgPyhbWfnL1+Q3h53Jp4rMo0eP0rJlS2677Ta+/vprypYty/bt2ylVqpRrm7feeosxY8Ywbdo0qlSpwrBhw2jXrh1bt271yLhwuXOP5iZpkfxwZkBiopWgiwVC8eKwe7fdUblzOp0cPnyYPXv2nDNFneRf7pzQeVEOE2+V9iccPX0CvHwZ2PeHvfGcTfnLcy6Uw87mU4OxDxkyhBUrVrB8+fI8HzfGEBMTw/PPP8+gQYMASE1NJSoqiqlTp/LAAw9c9P+40EDGZ8rJyTlvj0aRM5mTMOBm+OY4RAXD599BmXIXf97Vdvz4cZo0acJPP/1EyZJqaHU5goKCLvjrXzlMvNGv8+HBFyATeKkddPu33RGdS/nLMy6Ww87mU0Vm7dq1adeuHX/88QdLly6lQoUK9OnTh549ewKwa9currvuOjZu3OiafB6gVatWNGzYkH//+9xPRkZGBhkZGa7ltLQ0KlaseNEELZJfbzWHwWsgCFg6H2I72h1R3vJbnMjlUw4Tb5P2BzSuCjuyoHM0zD1QOHuTK3/ZoxAeCpdv165drrZJ33zzDb179+bZZ59l2rRpACQmJgLW2GhnioqKcj12tlGjRhEeHu66VayolsziOd/9E4ause6PebbwFphydSiHiTcxTniqpVVgVgqAyT8WzgJT7ONTh4PT6aRRo0aMHDmSG264gV69etGzZ0/Gjx9/2fscOnQoqamprtv+/fs9GLEUZbvjoetIa8Dix+vDU+/bHZHYTTlMvMmEbjBrn9W5Y9ZYiLzO7oiksPGpIrN8+fLUrl3bbV2tWrXYt28f8HeD9qSkJLdtkpKSztuI1eFwEBYW5nYTuVLph+HujvAXcGMojF0B6sQrymHiLTbOhAEzrftvdITYXvbGI4WTTxWZLVu2JCEhwW3d77//7prxoUqVKkRHRxMfH+96PC0tjTVr1hAbG3tVY5Wiyxjo0RQ2n4KyfvD591BM7dAF5TDxDil74b5HIQO4MwoGzrM7IimsfGoIo+eee44WLVowcuRIunTpwtq1a5k4cSITJ04EwM/PjwEDBvDaa69RrVo11/AfMTEx3HXXXTZHL0XFm11g9m7rw/f5u1Cxid0RSWGhHCaFnXHCEy1gVzZcGwDTVqodplyA8THz5883devWNQ6Hw9SsWdNMnDjR7XGn02mGDRtmoqKijMPhMG3atDEJCQn53n9qaqoBTGpqqqdDlyLgy/eN8cMYMGbcnXZHc2l07F8dymFSmI3uaOWvYIxZN9XuaPJPx709fGoIo6tBwyDI5fp1FcS2hGMGeleCsbvxqgYrOvZ9g/6OcrmWjoE2/SEHGNsVes+yO6L803FvDy/6ihPxXoeToVOcVWDe6oB/r0WfPhHxGgc3QtfnrAKzWxV4eobdEYk30NecSAHLzIT7msGuE1AFmLMQgqIu+jQRkUIhMx3ubwVJTqjrgPGr1Q5T8keHiUgBMgb6dIKleyAUmP8qlGljd1QiIvn3fAtYeQzCgbkLoEQhnPZWCicVmSIF6N0XYdI31gdt5u1QZ5jdEYmI5N+0XvCfn637/30Rro+zNx7xLioyRQrIvFnwwhvW/XcrQ4cv7I1HRORSrP8EnvrIuj/8Fuj0ur3xiPdRkSlSADash4e6gQGeCoFnVwAOu6MSEcmfpF/gru7WgOsdy8HL8Rd9isg5VGSKeNj+/dDxNjiRA2394INF4FfB7qhERPInMx3ubwl/5ECNIPjfWvD3qalb5GpRkSniQWlp0OFmOHQM6gCfvgdBt9gdlYhI/j3bFJanQRjwxVwIr2x3ROKtVGSKeEhWFtzbDrbshWjgq0chvL/dUYmI5N+4h2DCVvADZgyDmh3sjki8mYpMEQ8wBno9Ct+thhLAgiZQ6WO7oxIRyb/v34VnZlr3R7aFDq/aG494PxWZIh4w/CWYOgsCgE+jofHXQJDdUYmI5M+O7+G+QdaMPg9VhsFf2x2R+IJCUWR2796dZcuW2R2GyGWZOAH+NdK6P64Y3BEPlLE1JLmKlL/E26XshTvbw1EDTUvAxxs0o494RqE4jFJTU4mLi6NatWqMHDmSAwcO2B2SSL58+SX07m3dfxnoOReobWdEcrUpf4k3yzoJXRrDb5lwTQB8sRxCIu2OSnxFoSgyv/jiCw4cOEDv3r2ZPXs21157Le3bt+ezzz4jKyvL7vBE8rRiBXS9H5wGngBGjAFutzsqudqUv8RbGSc80wQWH7Haks//H5S/we6oxJcUiiIToGzZsgwcOJDNmzezZs0arr/+eh555BFiYmJ47rnn2L59u90hirj88gt0bA+nMqEjMKE3+D1jd1RiF+Uv8Ubv3n1GT/Kh0PABuyMSX1Noisxchw4dYvHixSxevJiAgADuuOMOtmzZQu3atXnvvffsDk+EPXugXRykHIMWwOx2EDjG7qikMFD+Em/x+WB44Uvr/rudoNNIe+MR31QoisysrCw+//xzOnbsSOXKlZkzZw4DBgzg4MGDTJs2je+++45PP/2UV1/VeApir6Qk+EcbOJhkDbY+vy4UnwNoNowiS/lLvM2qSdDtLWva2z51oP9cuyMSX1UovhrLly+P0+nkwQcfZO3atTRs2PCcbW677TYiIiJsiE7EkpIC7drCjl1wLfBNeYhcBITaHJjYSvlLvMmOeOjUE04BHcrCv39ST3IpOIWiyHzvvfe4//77KVas2Hm3iYiIYPfu3VcxKpG/padDhw6w+WeIAhaXhAqLAM1JXuQpf4m3+PM3uL09HDbQKARmbYbA8x+2IlesUBSZjzzyiN0hiJzXqVNw992wciVEAN8EwvXzgPp2RyaFgfKXeIP0ZOjQBHZmwbUBsHAVlCxvd1Ti63z6JPkbb7yBn58fAwYMcK07deoUffv2pXTp0pQsWZJ7772XpKQkG6OUwiwrC7p0gcWLrSE+vgYaTAVa2xuX+D7lL/GUrJPQpR6sS4fSfrBoHkQ3sDsqKQp8tshct24dEyZMoH5999NNzz33HPPnz2fOnDksXbqUgwcPcs8999gUpRRm2dnwyCMwfz4UA+YDzd8GHrY5MPF5yl/iKcYJPevDV8kQAiwYBzU62B2VFBU+WWQeP36chx9+mI8++ohSpUq51qempjJp0iTeffddWrduTePGjZkyZQorPJQ4ZgAAGe9JREFUV65k9erVee4rIyODtLQ0t5v4PqcTnngCZs+2piD/HLhtIPC8zYGJz/Nk/gLlsKJucAuYtgMCgE9fhOZP2R2RFCU+WWT27duXDh06EBcX57Z+/fr1ZGVlua2vWbMmlSpVYtWqVXnua9SoUYSHh7tuFStWLNDYxX5OJ/TqBdOnW4l5NnBHN2C0zYFJkeDJ/AXKYUXZWx1h9Brr/sePQcfXbQ1HiiCfKzJnzZrFhg0bGDVq1DmPJSYmEhwcfM5QIlFRUSQmJua5v6FDh5Kamuq67d+/v0DilsLB6bTmIp80yfpwfALc3QGYjA9+WqSw8XT+AuWwourjx2HwQuv+W7fDY1PsjUeKpkLRu9xT9u/fT//+/Vm8ePEFhxO5FA6HA4fD4ZF9SeHmdELfvjBxolVPTge63gx8inXNXKQAFUT+AuWwoujT56HXVOv+4Bvhha9sDUeKMJ86N7N+/XqSk5Np1KgRgYGBBAYGsnTpUsaMGUNgYCBRUVFkZmaSkpLi9rykpCSio6NtiloKA6cT+vSB8eOteXynAA81wurtU9ze2KRoUP4ST/jqX/Dwu9ZsPr1qwKjVWElNxAY+dSazTZs2bNmyxW3d448/Ts2aNRk8eDAVK1YkKCiI+Ph47r33XgASEhLYt28fsbGxdoQshYDTCU89BR9/bOXiqcCjNYFFQLitoUkRovwlV+r79+CelyEbeKgSjP1Zs/mIvXyqyAwNDaVu3bpu60qUKEHp0qVd63v06MHAgQOJjIwkLCyMZ555htjYWJo3b25HyGKznBzo0QOmTbNO608Dul0HxANl7Y1NihblL7kSKydCp4GQAXSOgqlbISDY7qikqPOpIjM/3nvvPfz9/bn33nvJyMigXbt2jB071u6wxAZZWfDoozBrltWLfDrwYEWsAjPG3thE8qL8JXlZOw1ufwrSgbaRMDsBgkrYHZUI+BljjN1BeJO0tDTCw8NJTU0lLCzM7nDkMmVkQNeuMG8eBPnBTAP3xgDLgOvsjq5w0rHvG/R39C3rP4G4RyDFwK3hsHA7FNdVmHPouLdHkTuTKZKeDvfcA99+Cw4/+MxAxyjge1RgiojX2DDz7wKzZSjM36YCUwoXFZlSpKSkQIcOsHIllPCHeU5oEwX8ANSwOTgRkXzaMAPiulkFZmxJ+HoblCxvd1Qi7lRkSpGRlAS33w6bNkFEACzMgRZRwBKgpt3RiYjkz0//g388ahWYzUvAoq0QWsHuqETOpcENpEjYvRtuuskqMKMCYGkOtIjGOoNZy+bgRETyafUkaHP6EnmLkvDNNgjTTKFSSKnIFJ+3eTO0aAE7dkCVQFiRA/UrAEvRGUwR8RrLPoR/PAlpwC1hsOg3FZhSuKnIFJ/2ww9wyy2QmAj1guDHbLiuMlYv8uo2Bycikk/fvgG394PjQOsI+Op3XSKXwk9FpvisWbOgXTtIS4NbgmBZFsRUA5YDVe2OTkQkf+YOhTuHwkngjrKwYAeUiLI7KpGLU5EpPscYGD0aHnwQMjPhviD4Jgsi6mGdwdTlJRHxEtOegvvegEzgvhiYuxNCStsdlUj+qMgUn5KdDf36wf/7f9Zy/0CYnQXFmmN18om2MTgRkUvw7t3w2ERwAo9fDzN3QnCo3VGJ5J+GMBKfkZYGDzwAX38Nfn7wnh/0zwbaAp8DJW0OUEQkH4wTXrwZ3lhpLQ+8AUavBX99Y4uX0SErPmHvXrjzTtiyBUKCYEYW3GWAB4BpQLDNAYqI5EPWSejVAKZut5ZH/QMGLwI/XXcUL6TDVrzeqlXQtKlVYEYXh6VZcBfAAOATVGCKiFc4ngidKlsFZgAw+TEY8q0KTPFeOnTFq02bBrfeCsnJ0CAc1p6AGwHeAt5FR7iIeIVDm6HVdbDoTygOfPESPD7F7qhEroy+gsUrZWfDwIHw2GNWD/K7S8GPqVAxGOvs5QuAn70xiojkxy9fQLPGsOEElPWDJR9Dx3/ZHZXIlVObTPE6hw9bwxN99521PCwcRhwF/0hgLnCLndGJiOTfotehy0twDKgeBF99Dde1sTsqEc9QkSleZeNGuPtuq6NPcQf81w/uTQWuBxYANWwOUEQknz58APrPhhysaSLn/gSR1eyOSsRzdLlcvMbkyRAbaxWY15WGNZlw7ymsM5erUYEpIl4h6wT0qQf9TheYj10Hi/9QgSm+R0WmFHonT8KTT0KPHpCRAR0qwLojUNcATwKLAc2AISJe4M/f4B8VYNwvVrPxN2+Hyb9rkHXxTSoypVDbvt06ezlpkjXA+qsx8OUBKBUA/BuYiIYoEhGvsHEW3FgXlqZAKDDvRfh/X2uIIvFdPnVojxo1ihtvvJHQ0FDKlSvHXXfdRUJCgts2p06dom/fvpQuXZqSJUty7733kpSUZFPEciEzZ0KjRrB5M5SNgG9DYdhB8C8NfAs8i3qQi09RDvNd03tDiwdhbw5cFwir58Gdr9sdlUjB8qkic+nSpfTt25fVq1ezePFisrKyaNu2Lenp6a5tnnvuOebPn8+cOXNYunQpBw8e5J577rExajlbejo88QQ89BAcPw6tqsCmVIhLA24AfgJa2xykSAFQDvM9mcehbz14dDycAtqXgXUJULuT3ZGJXAXGhyUnJxvALF261BhjTEpKigkKCjJz5sxxbbNt2zYDmFWrVuVrn6mpqQYwqampBRJzUbd+vTHVqxsDxvj5GTOsmjFZGGMwxjxmjDlhc4BFmI79q085zLvtWWFM0xJWPgNjht1kTHaG3VEVTTru7eFTZzLPlpqaCkBkZCQA69evJysri7i4ONc2NWvWpFKlSqxatSrPfWRkZJCWluZ2E8/LyYE334TmzeH336FCWfi+LLy6HQIdWG0vJwMhNgcqchUph3mvL1+CG26CtelQyg8WvAyvLocAtSGXIsRni0yn08mAAQNo2bIldevWBSAxMZHg4GAiIiLcto2KiiIxMTHP/YwaNYrw8HDXrWLFigUee1Gzeze0bg1DhkBWFtxTBzYfgVuTsca/XA30RO0vpUhRDvNOGWnwXCPo/DocNdC0BGxcBh1esTsykavPZ4vMvn378ssvvzBr1qwr2s/QoUNJTU113fbv3++hCMUY+OgjqF8fli2DkiVgck347Fco7QQeBNYDDW0OVMQGymHeJ+FriI2G9zdaywMbwfJEqHyTvXGJ2MUnZ/zp168fCxYsYNmyZVxzzTWu9dHR0WRmZpKSkuJ2JiApKYno6Og89+VwOHA4HAUec1Gzf7819uW331rLN9eCqQeg6m9ACWAM8Dg6eylFknKYdzFOmPgIDJwBJ4AyfjDlJej4qt2RidjLp85kGmPo168fc+fO5fvvv6dKlSpujzdu3JigoCDi4+Nd6xISEti3bx+xsbFXO9wiyemEceOgdm2rwCxWDN5uBEu2QdU0oDHW2csnUIEpRY5ymPdJ/Bk6lYenTxeYbUrB5nUqMEXAx85k9u3blxkzZjBv3jxCQ0NdbZTCw8MJCQkhPDycHj16MHDgQCIjIwkLC+OZZ54hNjaW5s2b2xy97/vtN+jVC5Yvt5Zb1ILJR6DGBqyfO0OB4UCQfTGK2Ek5zIsY+PQ56DMGjhhrTohRnWDA5+DvU9+sIlfA7u7tngTkeZsyZYprm5MnT5o+ffqYUqVKmeLFi5u7777bHDp0KN//h4ZBuHQnTxrz8svGBAdbw3iUKGHMv5sZk507NFE1Y0z+Rl8RG+nYL3jKYd4hcYsx91f4e2iiBsWM2fJ/dkclF6Lj3h5+xhhz9Utb75WWlkZ4eDipqamEhYXZHU6h98030K8f7NhhLd/RCMbuh8p/Yl0OHwC8BhS3L0bJHx37vkF/x8tnnPBJH+g/Ef4yEAC8eAu8tBCCS9odnVyIjnt76KS+FIg9e2DgQJg711ouXw7GVIR7159ualkT+BhoaVuIIiL5tmsJ9LkfvjliLTcoBpMnQaOH7I1LpDDzqY4/Yr/jx+Hll6FWLavADAiA526C347BfevBLwgYBmxEBaaIFHqZx2DkP6BOa6vAdACvtYV1R1RgilyMzmSKR+TkwPTp8M9/wsGD1rrbGsCYNKj74+mNbgbGAXVsClJE5BJ8+zo88wr8nmUtty4F42ZB9bb2xiXiLVRkyhUxxhqKaPBg2LzZWlflGng7Gu7+6fSl8XLAm0B3NCyRiBR6O7+D57vBvCRrOcof3n4aHv4A/HT9TyTfVGTKZVuzBoYOhSVLrOXwMHipATyzEhx/YB1dfYERQMR5dyMiUiik7ILX74cxGyATK4X1awQjvoBwzcYpcslUZMol27jRane5YIG1HBwMfW+Ef/4MpU+PgckdwNtALZuCFBHJp1N/wbhH4bWvrF7jAG3LwHtToXYHW0MT8Wo68S/5tn49dO4MjRpZBaa/PzzeDH4Pg3dXQOljQAPgG2AhKjBFpFDLPgGTH4XqZWHgQqvArO2Ar16DRckqMEWulM5kygUZA8uWwahR1piXAH5+8GBjGL4fqq85vWEV4FXgIfTTRUQKtewTMPNZeHUa7Mi21lUIgBGPwmPjIFBTvYt4hIpMyVN2tjUE0TvvWG0vwRqO6MEG8M/9UPOn0xteA/wTa67xYHtiFRHJj8xUmN4H3vj07+KyjB8M6Qx9pkCI2o6LeJSKTHFz9ChMngz/+Y81oDpAMQc8Vgte2AlVN5ze8BqsucafAIrZEqqISL6k7YGPesN738IBp7WujB883x76TYGS5WwNT8RnqcgUwGpvOX48fPIJnDxprSsTAX2ugT7bIGrT6Q2rA4OBbujMpYgUaru/hQ9egEk/Q9rpdeUD4PlO8NQEKFnW1vBEfJ6KzCIsJQVmzoSPP4YNG/5eX68CPBsAD++DkJTTK28GBgEdUZtLESm0ck7CN6/CuI9g4RE43Vmcmg4Y9Ch0exccmmdc5KpQkVnEZGXB4sXw3//CvHlw6pS1PjgI7q0IfQ5CywOnx0x3AA8AzwCNbQtZROSi9n0PU4bBlNWw1/n3+rblYMDz0O558A+wLz6RokhFZhGQnW31EP/0U/j8czh8+O/H6pSBHjnwyFEos+v0yupAL6wZespc/XhFRPIjNQH+7xWYvgB+OPb3WctSftC9CTz9JtS4zdYQRYo0FZk+6sQJ+O4762zll1+6F5blisMDwdA9BW44fPqsZShwP1ZHnhZo+kcRKZRStsLCt2DOAlh0BDLOeOy20tDjUbhnBISE2RWhiORSkekjjIHffrPGsvzmG2uqx4wzsm+kA+7xh/tPQusTEHgC63L47cCDwJ1AcVtCFxE5L5MNO76ArybBghXWGcvsMx6vHQIPtYZur0BlNesRKVRUZHoppxO2bYMff7QuhS9ZAocOuW9TORg6ZUJnoFXG6T92SaA9cBdWJx792heRwsRA4jJY+l/4fgl8txd2Od03qRMC97SE+5+Huu2sCSJEpPBRkekFjIF9+6w5w9evh7VrrVtKivt2xfzgZgNtsaYOr5V5+qp3LaAd0AGrl7hmsxCRQiJjL2z5AtYthjWbYOUh2H5WURkE3FQWOt4GHZ+F6i1tCVVELpGKTE8zWNdygi79qcePw+7dsGsXbN8OCdtg68/wyzZISz93++JAU6DV6VusOT0uek2sYvIWoDUQc3kvRUTEI05BegLsXAk7NsBvv8Cvu+GXI7A12/3yN1g/juuXhNvqQZu7odWTEFrKjsBF5EqoyPSwjEOwoQI4S4AzHLJDISMETgbB8QBIM5CSDX9lwp8nIfkkHEyHP9LhaNb59xsE1AYaYRWWNwL1gaBrgRtO3248/WBkwb5GEfFd3wyGedOhdBiUjoTwCAgNg+KhUKwEBBUD/9PfHDk5kJUBp05A+jE4lgpHU+CvFPgzBRKPwYETsD8bDl/g/4z0hyZR0LQetLgDmj8ApaKuyssVkQJUZIvMDz/8kNGjR5OYmEiDBg344IMPaNq06RXvNynB6pxN+unbJYoAqmKNIlQdqOUHtctCzaoQXPWMB2tgXQYPveKQRcTLFFT+AlizBsYdAg5ddNNLVioArg+FmhWgVk2o2wIadICK1dWuUsQXFckic/bs2QwcOJDx48fTrFkz3n//fdq1a0dCQgLlyl3ZJLZB1aHqteDvBD8nBPtDsB+EBECJQAgNglLFrFvZklAuFGJKQ0xZqFQRwqKwKs0yZ9w0gLCInFaQ+Qug1RPwchk48icc+QtSj8Pxk5CeCRnZkOUE5+kBKQP8IMgfHIFQMhhKFoOIUIgMh3JRUK4CxFSDSg2hUl2I0CVvkSLFzxhjLr6Zb2nWrBk33ngj//nPfwBwOp1UrFiRZ555hiFDhrhtm5GRQcYZYwGlpaVRsWJFUlNTCQtT12wpOtLS0ggPD9exb7NLyV+gHCYCyl92KXKzUGdmZrJ+/Xri4uJc6/z9/YmLi2PVqlXnbD9q1CjCw8Ndt4oVK17NcEVEXC41f4FymIjYp8gVmYcPHyYnJ4eoKPdW5VFRUSQmJp6z/dChQ0lNTXXd9u/ff7VCFRFxc6n5C5TDRMQ+RbJN5qVwOBw4HBpYUkS8k3KYiNilyJ3JLFOmDAEBASQlJbmtT0pKIjo62qaoREQuTvlLRLxJkTuTGRwcTOPGjYmPj+euu+4CrIbz8fHx9OvX76LPz+0nlZaWVqBxihQ2ucd8EewrWGhcaf4C5TApmpS/7FHkikyAgQMH0r17d5o0aULTpk15//33SU9P5/HHH7/oc48dOwagxvNSZB07dozw8HC7wyiyriR/gXKYFG3KX1dXkSwyu3btyp9//snLL79MYmIiDRs2ZNGiRec0ps9LTEwM+/fvJzQ0FL/zjB6cO0TI/v37NVSCB+l9LTj5eW+NMRw7doyYGM1TaqcryV+gHGYnva8F52LvrfKXPYrkOJkFTeNxFQy9rwVH762cScdDwdD7WnD03hZORa7jj4iIiIgUPBWZIiIiIuJxASNGjBhhdxC+KCAggFtvvZXAwCLZ7LXA6H0tOHpv5Uw6HgqG3teCo/e28FGbTBERERHxOF0uFxERERGPU5EpIiIiIh6nIlNEREREPE5FpoiIiIh4nIpMD/vwww+59tprKVasGM2aNWPt2rV2h+T1RowYgZ+fn9utZs2adofllZYtW8add95JTEwMfn5+fPHFF26PG2N4+eWXKV++PCEhIcTFxbF9+3abohU7KId5nnKYZyh/eR8VmR40e/ZsBg4cyPDhw9mwYQMNGjSgXbt2JCcn2x2a16tTpw6HDh1y3X788Ue7Q/JK6enpNGjQgA8//DDPx9966y3GjBnD+PHjWbNmDSVKlKBdu3acOnXqKkcqdlAOKzjKYVdO+csLGfGYpk2bmr59+7qWc3JyTExMjBk1apSNUXm/4cOHmwYNGtgdhs8BzNy5c13LTqfTREdHm9GjR7vWpaSkGIfDYWbOnGlHiHKVKYcVDOUwz1P+8g46k+khmZmZrF+/nri4ONc6f39/4uLiWLVqlY2R+Ybt27cTExND1apVefjhh9m3b5/dIfmc3bt3k5iY6HYMh4eH06xZMx3DRYByWMFSDitYyl+Fk4pMDzl8+DA5OTlERUW5rY+KiiIxMdGmqHxDs2bNmDp1KosWLWLcuHHs3r2bm2++mWPHjtkdmk/JPU51DBdNymEFRzms4Cl/FU6ae0kKvfbt27vu169fn2bNmlG5cmU+/fRTevToYWNkIiIXpxwmRZXOZHpImTJlCAgIICkpyW19UlIS0dHRNkXlmyIiIqhevTo7duywOxSfknuc6hgumpTDrh7lMM9T/iqcVGR6SHBwMI0bNyY+Pt61zul0Eh8fT2xsrI2R+Z7jx4+zc+dOypcvb3coPqVKlSpER0e7HcNpaWmsWbNGx3ARoBx29SiHeZ7yV+EUMGLEiBF2B+ErwsLCGDZsGBUrVsThcDBs2DA2bdrEpEmTKFmypN3hea1BgwbhcDgA2Lp1K08//TTJycmMHz+eEiVK2Byddzl+/Dhbt24lMTGRCRMm0KxZM0JCQsjMzCQiIoKcnBxGjhxJ7dq1yczM5Nlnn+XEiRN88MEHBAaqdY2vUw4rGMphnqH85YXs7t7uaz744ANTqVIlExwcbJo2bWpWr15td0her2vXrqZ8+fImODjYVKhQwXTt2tXs2LHD7rC80pIlSwxwzq179+7GGGsYkGHDhpmoqCjjcDhMmzZtTEJCgr1By1WlHOZ5ymGeofzlffyMMcauAldEREREfJPaZIqIiIiIx6nIFBERERGPU5EpIiIiIh6nIlNEREREPE5FpoiIiIh4nIpMEREREfE4FZkiIiIi4nEqMkVERETE41RkioiIiIjHqcgUEREREY9TkSkiIiIiHqciUwq9P//8k+joaEaOHOlat3LlSoKDg4mPj7cxMhGRC1P+kqLMzxhj7A5C5GK++uor7rrrLlauXEmNGjVo2LAhnTt35t1337U7NBGRC1L+kqJKRaZ4jb59+/Ldd9/RpEkTtmzZwrp163A4HHaHJSJyUcpfUhSpyBSvcfLkSerWrcv+/ftZv3499erVszskEZF8Uf6SokhtMsVr7Ny5k4MHD+J0OtmzZ4/d4YiI5JvylxRFOpMpXiEzM5OmTZvSsGFDatSowfvvv8+WLVsoV66c3aGJiFyQ8pcUVSoyxSu88MILfPbZZ2zevJmSJUvSqlUrwsPDWbBggd2hiYhckPKXFFW6XC6F3g8//MD777/P9OnTCQsLw9/fn+nTp7N8+XLGjRtnd3giIuel/CVFmc5kioiIiIjH6UymiIiIiHicikwRERER8TgVmSIiIiLicSoyRURERMTjVGSKiIiIiMepyBQRERERj1ORKSIiIiIepyJTRERERDxORaaIiIiIeJyKTBERERHxOBWZIiIiIuJx/x+KOJBlPTKR2AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True function: y= 2 - x + x^2\n",
      "Learnt function: y_pred = 1.8918471336364746 + -0.9629372358322144*x + 0.9970840215682983*x^2\n",
      "Model has more or less converged to true underlying function\n"
     ]
    }
   ],
   "source": [
    "# Try quadratic model architecture:\n",
    "# y_pred = w0 + w1*x + w2*x^2\n",
    "w0 = torch.randn(1, requires_grad=True)\n",
    "w1 = torch.randn(1, requires_grad=True)\n",
    "w2 = torch.randn(1, requires_grad=True)\n",
    "params = [w0, w1, w2]\n",
    "\n",
    "plt.figure()\n",
    "i = 1\n",
    "\n",
    "# Train model iteratively\n",
    "# Run with very low learning rate\n",
    "# to prevent exploding gradients\n",
    "learning_rate = 1e-4\n",
    "num_steps = 200000\n",
    "plot_steps = [0, 50, 100, 199999]\n",
    "for step in range(num_steps):\n",
    "    # quadratic model architecture:\n",
    "    # y_pred = w0 + w1*x + w2*x^2\n",
    "    y_pred = params[0] + params[1] * x + params[2] * (x**2)\n",
    "\n",
    "    # Periodically plot the true function and\n",
    "    # current approximation to check how we are doing \n",
    "    if step in plot_steps:\n",
    "        draw_subplot(i, step, draw_parabola, \n",
    "                     {\"w0\": 2, \"w1\": -1, \"w2\": 1},\n",
    "                    draw_parabola,\n",
    "                    {\"w0\": params[0].data.numpy()[0],\n",
    "                     \"w1\": params[1].data.numpy()[0],\n",
    "                     \"w2\": params[2].data.numpy()[0],\n",
    "                     \"color\":\"blue\",\n",
    "                     \"label\":\"y_pred=%0.2f+%0.2fx+%0.2fx^2\"\n",
    "                           %(params[0].data.numpy()[0], \n",
    "                             params[1].data.numpy()[0],\n",
    "                             params[2].data.numpy()[0])} \n",
    "                    )\n",
    "        i+=1\n",
    "        \n",
    "    # Mean Squared Error (M.S.E)\n",
    "    # i.e (y_pred - y_obs)^2\n",
    "    mean_squared_error = torch.mean((y_pred -\n",
    "                                     y_obs) ** 2)\n",
    "    \n",
    "    # Back propogate. Computes the partial derivative\n",
    "    # of error with respect to each variable and stores it\n",
    "    # within the grad field of the variable.\n",
    "    mean_squared_error.backward()\n",
    "    if step % 20000 == 0:\n",
    "        print(\"Step {}:\\nw0 = {} w1 = {} w2 = {}\\n\"\n",
    "              \"MSE Error = {}\"\\\n",
    "              .format(step, params[0].data, params[1].data,\n",
    "                      params[2].data, mean_squared_error))\n",
    "        print(\"Gradient of w0: {} \\nGradient of w1: {}\\n\"\n",
    "              \"Gradient of w1: {}\"\\\n",
    "              .format(params[0].grad, params[1].grad,\n",
    "                      params[2].grad))\n",
    "    \n",
    "    # Crucial step, adjust the parameters (weights and bias)\n",
    "    # using the gradients (partial derivatives) computed during\n",
    "    # the call to backward() above \n",
    "    update_parameters(params, learning_rate)\n",
    "    \n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"True function: y= 2 - x + x^2\")\n",
    "print(\"Learnt function: y_pred = {} + {}*x + {}*x^2\"\\\n",
    "      .format(params[0].data.numpy()[0],\n",
    "              params[1].data.numpy()[0],\n",
    "              params[2].data.numpy()[0]))\n",
    "print(\"Model has more or less converged to \"\n",
    "      \"true underlying function\")   "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
